The status of our basic understanding of the physics and structure of glasses is presented in the... more The status of our basic understanding of the physics and structure of glasses is presented in the light of recent developments in the experimental, phenomenological, and numerical approach to the description of real systems. Spontaneous and induced dynamic heterogeneities appear in the supercooled state of liquids and become frozen intact below the glass transition point. In most cases, mesoscopic heterogeneities due to partial microphase separation are frozen in glasses. Thus, glasses can be described as dynamically arrested heterogeneous supercooled liquids with more solid-like and liquid-like nanoscale regions. The critical issue is that, depending on material type and temperature, the heterogeneities exhibit different size distributions with the solid-like regions probably displaying a degree of hidden quasi-order. This scenario naturally explains some of the important physical properties of real glasses.
We study phase transitions in uniformly frustrated SU(N)-symmetric (2+ǫ)dimensional lattice model... more We study phase transitions in uniformly frustrated SU(N)-symmetric (2+ǫ)dimensional lattice models describing type-II superconductors near the upper critical magnetic field Hc2(T ). The low-temperature renormalization-group approach is employed for calculating the beta-function β(T, f) with f an arbitrary rational magnetic frustration. The phase-boundary line Hc2(T ) is the ultraviolet-stable fixed point found from the equation β(T, f) = 0, the corresponding critical exponents being identical to those of the non-frustrated continuum system. The critical properties of the SU(N)-symmetric complex Ginzburg-Landau (GL) model are then examined in (4 + ǫ) dimensions. The possibility of a continuous phase transition into the mixed state in such a model is suggested. PACS numbers: 74.60Ge, 74.60Ec Typeset using REVTEX
We show that the exact beta-function β(g) in the continuous 2D gΦ4 model possesses the Kramers-Wa... more We show that the exact beta-function β(g) in the continuous 2D gΦ4 model possesses the Kramers-Wannier duality symmetry. The duality symmetry transformation g̃ = d(g) such that β(d(g)) = d′(g)β(g) is constructed and the approximate values of g∗ computed from the duality equation d(g∗) = g∗ are shown to agree with the available numerical results. The calculation of the beta-function β(g) for the 2D scalar gΦ4 field theory based on the strong coupling expansion is developed and the expansion of β(g) in powers of g−1 is obtained up to order g−8. The numerical values calculated for the renormalized coupling constant g∗ + are in reasonable good agreement with the best modern estimates recently obtained from the high-temperature series expansion and with those known from the perturbative four-loop renormalization-group calculations. The application of Cardy’s theorem for calculating the renormalized isothermal coupling constant gc of the 2D Ising model and the related universal critical a...
The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder des... more The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the so-called generalized Ashkin-Teller model (GATM) is studied. In the critical region this model is shown to be described by a multifermion field theory similar to the Gross-Neveu model with a few independent quartic coupling constants. Renormalization group calculations are used to obtain the temperature dependence near the critical point of some thermodynamic quantities and the large distance behavior of the two-spin correlation function. The equation of state at criticality is also obtained in this framework. We find that random models described by the GATM belong to the same universality class as that of the two-dimensional Ising model. The critical exponent ν of the correlation length for the 3-and 4-state randombond Potts models is also calculated in a 3-loop approximation. We show that this exponent is given by an apparently convergent series in ǫ = c − 1 2 (with c the central charge of the Potts model) and that the numerical values of ν are very close to that of the 2D Ising model. This work therefore supports the conjecture (valid only approximately for the 3-and 4-state Potts models) of a superuniversality for the 2D disordered models with discrete symmetries.
We present a theory for the decay of a supercurrent through nucleation of vortex-antivortex pairs... more We present a theory for the decay of a supercurrent through nucleation of vortex-antivortex pairs in a two-dimensional superconductor in the presence of dissipation and of a periodic pinning potential. Through a powerful quantum electrodynamics formulation of the problem we show that the nucleation rate develops oscillations in its current-density dependence which are connected to the pinning periodicity. A remnant of the dissipation-driven localization transition is present, and an estimate of the nucleation rate suggests that these effects might be observable in real thin superconductors.
We investigate the phenomenon of the decay of a supercurrent due to the zero-temperature quantum ... more We investigate the phenomenon of the decay of a supercurrent due to the zero-temperature quantum tunneling of vortices from the edge in a thin superconducting film in the absence of an external magnetic field. An explicit formula is derived for the tunneling rate of vortices, which are subject to the Magnus force induced by the supercurrent, through the Coulomb-like potential barrier binding them to the film's edge. Our approach ensues from the non-relativistic version of a Schwinger-type calculation for the decay of the 2D vacuum previously employed for describing vortex-antivortex pair-nucleation in the bulk of the sample. In the dissipation-dominated limit, our explicit edge-tunneling formula yields numerical estimates which are compared with those obtained for bulk-nucleation to show that both mechanisms are possible for the decay of a supercurrent.
The second-order phase transition of a weakly disordered system in 2 + e dimensions is investigat... more The second-order phase transition of a weakly disordered system in 2 + e dimensions is investigated by means of the low-temperature renormalization group technique. It is shown that there are two fixed points: the Migdal-Polyakov and the unphysical ones. As the Migdal-Polyakov fixed point is always stable it is concluded that the disordered and the ordered systems have the same critical exponents. These results agree with the Harris hypothesis, which predicts that phase transitions with positive value of a do not occur in the presence of quenched disorder. The effects of the long-range exchange interaction on the critical behaviour of the quenched system in 6 + E dimensions are also discussed. The criteria for the concentration of nonmagnetic impurities in the systems under consideration are established. MCCJIenOBaH @a3OBbl& ITepeXOX BTOpOrO p O n a CJIa60-HeyIlOpHAO9eHHO& CHCTeMbI B 2 + &
Nous présentons une étude auto-cohérente du franchissement du seuil dans un laser monomode à mili... more Nous présentons une étude auto-cohérente du franchissement du seuil dans un laser monomode à milieu actif homogène. Nous obtenons pour la puissance, la longueur d'onde et la largeur de raie des expressions universelles en coordonnées normalisées, continûment valables de part et d'autre du seuil.
The density of states of Dirac fermions with a random mass on a two-dimensional lattice is consid... more The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in the regime where all states are localized. We make use of a weak-disorder expansion in the parameter g/m 2 , where g is the strength of disorder and m the average Dirac mass for the case in which the evaluation of the (supersymmetric) integrals corresponds to non-uniform solutions of the saddle point equation. The resulting density of states has tails which deviate from the typical pure Gaussian form by an analytic prefactor.
Ordinary multi-component silicate glasses belong to a class of amorphous insulators normally disp... more Ordinary multi-component silicate glasses belong to a class of amorphous insulators normally displaying no special form of magnetism, save for the Larmor dominant diamagnetism from the constituent atoms’ core electrons and the extrinsic Langevin paramagnetism due to the ubiquitous Fe-group dilute paramagnetic impurities. Here we show that the macroscopic magnetisation of three case-study glass types measured in a SQUID-magnetometer cannot be explained solely by means of the Larmor-Langevin contributions. In particular, we reveal a novel intrinsic contribution to the bulk magnetisation due to the amorphous structure itself, a contribution that is peculiar both in its temperature and magnetic-field dependence and represents the first true magnetic effect in nominally non-magnetic glasses. The only theoretical interpretation we know of for such an effect and which can consistently explain the experimental data demands the re-thinking of the atomic organisation of glasses at the nanomet...
This is a short account of the basic principles of a comprehensive theory of the vitreous state, ... more This is a short account of the basic principles of a comprehensive theory of the vitreous state, looking at glasses and their eventual > into a liquid state (the inverse glass >) from the perspective of their low-temperature properties, then working all the way up to the melting temperature (and back again). The theory is still in the making, so only essential guidelines will be provided. There appears to be no ideal-glass transition, no ideal-glass state, but a first theoretical justification of the Vogel-Fulcher-Tamman law can be provided, making glasses truly fascinating quantum as well as topological substances.
In a recent manuscript, the discovery of a new phenomenon in glasses has been reported: glass par... more In a recent manuscript, the discovery of a new phenomenon in glasses has been reported: glass paramagnetism, that is the intrinsic magnetisation developed by a substance that has failed to crystallise in a temperature quench when placed in an external magnetic field. The field(H) and especially the temperature(T ) dependence of the intrinsic magnetisation Mintr = Mintr(H,T ) is very unexpected, with broad peaks developing for high H/T and marked T oscillations at fixed H for intermediate-to-high temperatures. In this work we present details on the samples, new data for other glassy systems and especially the theoretical background that is capable of explaining most of the experimental data. New phenomena are however emerging from these data, for example a deviation from the Curie-like behaviour of the magnetic susceptibility (Mintr/H at low fields) due to the glassy structure alone as well as evidence for new and intriguing quantum coherence effects at the lowest temperatures.
Puzzling observations of both thermal and dielectric responses in multi-silicate glasses at low t... more Puzzling observations of both thermal and dielectric responses in multi-silicate glasses at low temperatures T to static magnetic fields B have been reported in the last decade and call for an extension of the standard two-level systems tunneling model. An explanation is proposed, capable of capturing at the same time the T- and B-dependence of the specific heat C_p and of the dielectric constant ϵ in these glasses. This theory points to the existence of anomalous multi-welled tunneling systems in the glasses -- alongside the standard two-level systems -- and indications are given for glasses which should achieve larger electric magnetocapacitive enhancements.
The discovery of magnetic and compositional effects in the low temperature properties of multicom... more The discovery of magnetic and compositional effects in the low temperature properties of multicomponent glasses has prompted the need to extend the standard two-level systems (2LSs) tunneling model. A possible extension [1] assumes that a subset of tunneling quasi-particles is moving in a threewelled potential (TWP) associated with the ubiquitous inhomogeneities of the disordered atomic structure of the glass. We show that within an alternative, cellular description of the intermediate-range atomic structure of glasses the tunneling TWP can be fully justified. We then review how the experimentally discovered magnetic effects can be explained within the approach where only localized atomistic tunneling 2LSs and quasi-particles tunneling in TWPs are allowed. We discuss the origin of the magnetic effects in the heat capacity, dielectric constant (real and imaginaryi parts), polarization echo and SQUID magnetization in several glassy systems. We conclude by commenting on a strategy to reveal the mentioned tunneling states (2LSs and TWPs) by means of atomistic computer simulations and discuss the microscopic nature of the tunneling states in the context of the potential energy landscape of glass-forming systems.
Quasi-elastic and inelastic neutron scattering measurements have been performed on the magnetic s... more Quasi-elastic and inelastic neutron scattering measurements have been performed on the magnetic system (CD3) 4NMn (1-x) CuxCl3 with x= 0.03 and 0.08. A decrease of the one-dimensional correlation length ξ with respect to pure TMMC is observed and discussed. ...
The critical behavior of 2D anisotropic systems with weak quenched disorder described by the so--... more The critical behavior of 2D anisotropic systems with weak quenched disorder described by the so--called generalized Ashkin--Teller model (GATM), including the Ising model with random bonds, the dilute Baxter model, the impure N--color Ashkin--Teller model, and minimal conformal field theory models (MCFTM) with c<1 (c is the central charge) perturbed by randomness is discussed. All these models except MCFTM were
2014 L'importance des corrections de gonflement dans la théorie des champs décrivant une chaîne p... more 2014 L'importance des corrections de gonflement dans la théorie des champs décrivant une chaîne polyélectrolyte isolée sans écrantage est examinée à partir de la théorie de renormalisation des opérateurs composés. On montre que ces corrections deviennent pertinentes en dessous d'une dimension non spécifiée d* 6, où le résultat exact 03BD = 2/(d 2014 2) perd sa validité, ainsi que sa signification physique, et un nouveau modèle décrit le système. Abstract. 2014 The importance of swelling corrections in the field-theoretic model describing an isolated, unscreened polyelectrolyte chain below six dimensions is examined using the renormalization theory of higher composite operators. Evidence is given of the relevance of these corrections below an unspecified dimension d* 6, when the unphysical exact result 03BD = 2/(d-2) breaks down and the system is described by a new model.
We investigate the phenomenon of decay of a supercurrent in a superconducting thin film in the ab... more We investigate the phenomenon of decay of a supercurrent in a superconducting thin film in the absence of an applied magnetic field. The resulting zero-temperature resistance derives from two equally possible mechanisms: 1) quantum tunneling of vortices from the edges of the sample; and 2) homogeneous quantum nucleation of vortex-antivortex pairs in the bulk of the sample, arising from the instability of the Magnus field's "vacuum". We study both situations in the case where quantum dissipation dominates over the inertia of the vortices. We find that the vortex tunneling and nucleation rates have a very rapid dependence on the current density driven through the sample. Accordingly, whilst normally the superconductor is essentially resistancefree, for the high current densities that can be reached in high-T c films a measurable resistance might develop. We show that edge-tunneling appears favoured, but the presence of pinning centres and of thermal fluctuations leads to an enhancement of the nucleation rates. In the case where a periodic pinning potential is artificially introduced in the sample, we show that current-oscillations will develop indicating an effect specific to the nucleation mechanism where the vortex pair-production rate, thus the resistance, becomes sensitive to the corrugation of the pinning substrate. In all situations, we give estimates for the observability of the studied phenomena.
The question of the universality of the longitudinal peak conductivity at the integer quantum Hal... more The question of the universality of the longitudinal peak conductivity at the integer quantum Hall transition is considered. For this purpose, a system of 2D Dirac fermions with random mass characterised by variance g is proposed as a model which undergoes a quantum Hall transition. Whilst for some specific models the longitudinal peak conductivity σxx was found to be universal (in agreement with the conjecture of Lee et al. as well as with some numerical work), we find that σxx is reduced by a factor (1 + g/2π) −1 , at least for small g. This provides some theoretical evidence for the nonuniversality of σxx, as observed in a number of experiments.
The status of our basic understanding of the physics and structure of glasses is presented in the... more The status of our basic understanding of the physics and structure of glasses is presented in the light of recent developments in the experimental, phenomenological, and numerical approach to the description of real systems. Spontaneous and induced dynamic heterogeneities appear in the supercooled state of liquids and become frozen intact below the glass transition point. In most cases, mesoscopic heterogeneities due to partial microphase separation are frozen in glasses. Thus, glasses can be described as dynamically arrested heterogeneous supercooled liquids with more solid-like and liquid-like nanoscale regions. The critical issue is that, depending on material type and temperature, the heterogeneities exhibit different size distributions with the solid-like regions probably displaying a degree of hidden quasi-order. This scenario naturally explains some of the important physical properties of real glasses.
We study phase transitions in uniformly frustrated SU(N)-symmetric (2+ǫ)dimensional lattice model... more We study phase transitions in uniformly frustrated SU(N)-symmetric (2+ǫ)dimensional lattice models describing type-II superconductors near the upper critical magnetic field Hc2(T ). The low-temperature renormalization-group approach is employed for calculating the beta-function β(T, f) with f an arbitrary rational magnetic frustration. The phase-boundary line Hc2(T ) is the ultraviolet-stable fixed point found from the equation β(T, f) = 0, the corresponding critical exponents being identical to those of the non-frustrated continuum system. The critical properties of the SU(N)-symmetric complex Ginzburg-Landau (GL) model are then examined in (4 + ǫ) dimensions. The possibility of a continuous phase transition into the mixed state in such a model is suggested. PACS numbers: 74.60Ge, 74.60Ec Typeset using REVTEX
We show that the exact beta-function β(g) in the continuous 2D gΦ4 model possesses the Kramers-Wa... more We show that the exact beta-function β(g) in the continuous 2D gΦ4 model possesses the Kramers-Wannier duality symmetry. The duality symmetry transformation g̃ = d(g) such that β(d(g)) = d′(g)β(g) is constructed and the approximate values of g∗ computed from the duality equation d(g∗) = g∗ are shown to agree with the available numerical results. The calculation of the beta-function β(g) for the 2D scalar gΦ4 field theory based on the strong coupling expansion is developed and the expansion of β(g) in powers of g−1 is obtained up to order g−8. The numerical values calculated for the renormalized coupling constant g∗ + are in reasonable good agreement with the best modern estimates recently obtained from the high-temperature series expansion and with those known from the perturbative four-loop renormalization-group calculations. The application of Cardy’s theorem for calculating the renormalized isothermal coupling constant gc of the 2D Ising model and the related universal critical a...
The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder des... more The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the so-called generalized Ashkin-Teller model (GATM) is studied. In the critical region this model is shown to be described by a multifermion field theory similar to the Gross-Neveu model with a few independent quartic coupling constants. Renormalization group calculations are used to obtain the temperature dependence near the critical point of some thermodynamic quantities and the large distance behavior of the two-spin correlation function. The equation of state at criticality is also obtained in this framework. We find that random models described by the GATM belong to the same universality class as that of the two-dimensional Ising model. The critical exponent ν of the correlation length for the 3-and 4-state randombond Potts models is also calculated in a 3-loop approximation. We show that this exponent is given by an apparently convergent series in ǫ = c − 1 2 (with c the central charge of the Potts model) and that the numerical values of ν are very close to that of the 2D Ising model. This work therefore supports the conjecture (valid only approximately for the 3-and 4-state Potts models) of a superuniversality for the 2D disordered models with discrete symmetries.
We present a theory for the decay of a supercurrent through nucleation of vortex-antivortex pairs... more We present a theory for the decay of a supercurrent through nucleation of vortex-antivortex pairs in a two-dimensional superconductor in the presence of dissipation and of a periodic pinning potential. Through a powerful quantum electrodynamics formulation of the problem we show that the nucleation rate develops oscillations in its current-density dependence which are connected to the pinning periodicity. A remnant of the dissipation-driven localization transition is present, and an estimate of the nucleation rate suggests that these effects might be observable in real thin superconductors.
We investigate the phenomenon of the decay of a supercurrent due to the zero-temperature quantum ... more We investigate the phenomenon of the decay of a supercurrent due to the zero-temperature quantum tunneling of vortices from the edge in a thin superconducting film in the absence of an external magnetic field. An explicit formula is derived for the tunneling rate of vortices, which are subject to the Magnus force induced by the supercurrent, through the Coulomb-like potential barrier binding them to the film's edge. Our approach ensues from the non-relativistic version of a Schwinger-type calculation for the decay of the 2D vacuum previously employed for describing vortex-antivortex pair-nucleation in the bulk of the sample. In the dissipation-dominated limit, our explicit edge-tunneling formula yields numerical estimates which are compared with those obtained for bulk-nucleation to show that both mechanisms are possible for the decay of a supercurrent.
The second-order phase transition of a weakly disordered system in 2 + e dimensions is investigat... more The second-order phase transition of a weakly disordered system in 2 + e dimensions is investigated by means of the low-temperature renormalization group technique. It is shown that there are two fixed points: the Migdal-Polyakov and the unphysical ones. As the Migdal-Polyakov fixed point is always stable it is concluded that the disordered and the ordered systems have the same critical exponents. These results agree with the Harris hypothesis, which predicts that phase transitions with positive value of a do not occur in the presence of quenched disorder. The effects of the long-range exchange interaction on the critical behaviour of the quenched system in 6 + E dimensions are also discussed. The criteria for the concentration of nonmagnetic impurities in the systems under consideration are established. MCCJIenOBaH @a3OBbl& ITepeXOX BTOpOrO p O n a CJIa60-HeyIlOpHAO9eHHO& CHCTeMbI B 2 + &
Nous présentons une étude auto-cohérente du franchissement du seuil dans un laser monomode à mili... more Nous présentons une étude auto-cohérente du franchissement du seuil dans un laser monomode à milieu actif homogène. Nous obtenons pour la puissance, la longueur d'onde et la largeur de raie des expressions universelles en coordonnées normalisées, continûment valables de part et d'autre du seuil.
The density of states of Dirac fermions with a random mass on a two-dimensional lattice is consid... more The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in the regime where all states are localized. We make use of a weak-disorder expansion in the parameter g/m 2 , where g is the strength of disorder and m the average Dirac mass for the case in which the evaluation of the (supersymmetric) integrals corresponds to non-uniform solutions of the saddle point equation. The resulting density of states has tails which deviate from the typical pure Gaussian form by an analytic prefactor.
Ordinary multi-component silicate glasses belong to a class of amorphous insulators normally disp... more Ordinary multi-component silicate glasses belong to a class of amorphous insulators normally displaying no special form of magnetism, save for the Larmor dominant diamagnetism from the constituent atoms’ core electrons and the extrinsic Langevin paramagnetism due to the ubiquitous Fe-group dilute paramagnetic impurities. Here we show that the macroscopic magnetisation of three case-study glass types measured in a SQUID-magnetometer cannot be explained solely by means of the Larmor-Langevin contributions. In particular, we reveal a novel intrinsic contribution to the bulk magnetisation due to the amorphous structure itself, a contribution that is peculiar both in its temperature and magnetic-field dependence and represents the first true magnetic effect in nominally non-magnetic glasses. The only theoretical interpretation we know of for such an effect and which can consistently explain the experimental data demands the re-thinking of the atomic organisation of glasses at the nanomet...
This is a short account of the basic principles of a comprehensive theory of the vitreous state, ... more This is a short account of the basic principles of a comprehensive theory of the vitreous state, looking at glasses and their eventual > into a liquid state (the inverse glass >) from the perspective of their low-temperature properties, then working all the way up to the melting temperature (and back again). The theory is still in the making, so only essential guidelines will be provided. There appears to be no ideal-glass transition, no ideal-glass state, but a first theoretical justification of the Vogel-Fulcher-Tamman law can be provided, making glasses truly fascinating quantum as well as topological substances.
In a recent manuscript, the discovery of a new phenomenon in glasses has been reported: glass par... more In a recent manuscript, the discovery of a new phenomenon in glasses has been reported: glass paramagnetism, that is the intrinsic magnetisation developed by a substance that has failed to crystallise in a temperature quench when placed in an external magnetic field. The field(H) and especially the temperature(T ) dependence of the intrinsic magnetisation Mintr = Mintr(H,T ) is very unexpected, with broad peaks developing for high H/T and marked T oscillations at fixed H for intermediate-to-high temperatures. In this work we present details on the samples, new data for other glassy systems and especially the theoretical background that is capable of explaining most of the experimental data. New phenomena are however emerging from these data, for example a deviation from the Curie-like behaviour of the magnetic susceptibility (Mintr/H at low fields) due to the glassy structure alone as well as evidence for new and intriguing quantum coherence effects at the lowest temperatures.
Puzzling observations of both thermal and dielectric responses in multi-silicate glasses at low t... more Puzzling observations of both thermal and dielectric responses in multi-silicate glasses at low temperatures T to static magnetic fields B have been reported in the last decade and call for an extension of the standard two-level systems tunneling model. An explanation is proposed, capable of capturing at the same time the T- and B-dependence of the specific heat C_p and of the dielectric constant ϵ in these glasses. This theory points to the existence of anomalous multi-welled tunneling systems in the glasses -- alongside the standard two-level systems -- and indications are given for glasses which should achieve larger electric magnetocapacitive enhancements.
The discovery of magnetic and compositional effects in the low temperature properties of multicom... more The discovery of magnetic and compositional effects in the low temperature properties of multicomponent glasses has prompted the need to extend the standard two-level systems (2LSs) tunneling model. A possible extension [1] assumes that a subset of tunneling quasi-particles is moving in a threewelled potential (TWP) associated with the ubiquitous inhomogeneities of the disordered atomic structure of the glass. We show that within an alternative, cellular description of the intermediate-range atomic structure of glasses the tunneling TWP can be fully justified. We then review how the experimentally discovered magnetic effects can be explained within the approach where only localized atomistic tunneling 2LSs and quasi-particles tunneling in TWPs are allowed. We discuss the origin of the magnetic effects in the heat capacity, dielectric constant (real and imaginaryi parts), polarization echo and SQUID magnetization in several glassy systems. We conclude by commenting on a strategy to reveal the mentioned tunneling states (2LSs and TWPs) by means of atomistic computer simulations and discuss the microscopic nature of the tunneling states in the context of the potential energy landscape of glass-forming systems.
Quasi-elastic and inelastic neutron scattering measurements have been performed on the magnetic s... more Quasi-elastic and inelastic neutron scattering measurements have been performed on the magnetic system (CD3) 4NMn (1-x) CuxCl3 with x= 0.03 and 0.08. A decrease of the one-dimensional correlation length ξ with respect to pure TMMC is observed and discussed. ...
The critical behavior of 2D anisotropic systems with weak quenched disorder described by the so--... more The critical behavior of 2D anisotropic systems with weak quenched disorder described by the so--called generalized Ashkin--Teller model (GATM), including the Ising model with random bonds, the dilute Baxter model, the impure N--color Ashkin--Teller model, and minimal conformal field theory models (MCFTM) with c<1 (c is the central charge) perturbed by randomness is discussed. All these models except MCFTM were
2014 L'importance des corrections de gonflement dans la théorie des champs décrivant une chaîne p... more 2014 L'importance des corrections de gonflement dans la théorie des champs décrivant une chaîne polyélectrolyte isolée sans écrantage est examinée à partir de la théorie de renormalisation des opérateurs composés. On montre que ces corrections deviennent pertinentes en dessous d'une dimension non spécifiée d* 6, où le résultat exact 03BD = 2/(d 2014 2) perd sa validité, ainsi que sa signification physique, et un nouveau modèle décrit le système. Abstract. 2014 The importance of swelling corrections in the field-theoretic model describing an isolated, unscreened polyelectrolyte chain below six dimensions is examined using the renormalization theory of higher composite operators. Evidence is given of the relevance of these corrections below an unspecified dimension d* 6, when the unphysical exact result 03BD = 2/(d-2) breaks down and the system is described by a new model.
We investigate the phenomenon of decay of a supercurrent in a superconducting thin film in the ab... more We investigate the phenomenon of decay of a supercurrent in a superconducting thin film in the absence of an applied magnetic field. The resulting zero-temperature resistance derives from two equally possible mechanisms: 1) quantum tunneling of vortices from the edges of the sample; and 2) homogeneous quantum nucleation of vortex-antivortex pairs in the bulk of the sample, arising from the instability of the Magnus field's "vacuum". We study both situations in the case where quantum dissipation dominates over the inertia of the vortices. We find that the vortex tunneling and nucleation rates have a very rapid dependence on the current density driven through the sample. Accordingly, whilst normally the superconductor is essentially resistancefree, for the high current densities that can be reached in high-T c films a measurable resistance might develop. We show that edge-tunneling appears favoured, but the presence of pinning centres and of thermal fluctuations leads to an enhancement of the nucleation rates. In the case where a periodic pinning potential is artificially introduced in the sample, we show that current-oscillations will develop indicating an effect specific to the nucleation mechanism where the vortex pair-production rate, thus the resistance, becomes sensitive to the corrugation of the pinning substrate. In all situations, we give estimates for the observability of the studied phenomena.
The question of the universality of the longitudinal peak conductivity at the integer quantum Hal... more The question of the universality of the longitudinal peak conductivity at the integer quantum Hall transition is considered. For this purpose, a system of 2D Dirac fermions with random mass characterised by variance g is proposed as a model which undergoes a quantum Hall transition. Whilst for some specific models the longitudinal peak conductivity σxx was found to be universal (in agreement with the conjecture of Lee et al. as well as with some numerical work), we find that σxx is reduced by a factor (1 + g/2π) −1 , at least for small g. This provides some theoretical evidence for the nonuniversality of σxx, as observed in a number of experiments.
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Papers by Giancarlo Jug