All Questions
Tagged with scale-invariance statistical-mechanics
11 questions
5
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1
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Difficulty with a scaling argument
I am trying to make sense of an argument in this paper, "Fracture strength: Stress concentration, extreme value statistics and the fate of the Weibull distribution".
The paper deals with how ...
- 555
9
votes
4
answers
695
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Is entropy scale-invariant?
The most common definition I’ve heard of entropy in physics is the number of micro-states for a given macro-state. Most examples use the atomic scale as the micro-setting and some kind of simple, ...
5
votes
1
answer
564
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Intuition behind power-law scale invariance
I have seen this notion of a scale-invariant power law curve exhibiting the property that $f(cx) = a(cx)^{-k} = c^{-k}f(x)$, and I am confused about how I should be thinking of this as "scale-...
- 725
0
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0
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Derivation of the Ising free energy close to a critical point
In "Statistical physics of fields" Mehran Kardar states that the Ising free energy scales with,
$$
f(t,h)\sim t^\alpha g_f\left(\frac{h}{t^\Delta}\right),
$$
wherein $t=\vert T-T_c\vert/T_c$ ...
- 573
16
votes
3
answers
1k
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Why does Critical Points have fluctuations on all scales (Infinite correlation length)?
I have been studying statistical field theory for a while and I still haven't found a physical explanation for this question. Every answer seems to be kind of circular. Basically something like this: &...
- 4,737
7
votes
2
answers
473
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Is the Landau free energy scale-invariant at the critical point?
My question is different but based on the same quote from Wikipedia as here. According to Wikipedia,
In statistical mechanics, scale invariance is a feature of phase transitions. The key ...
- 27.2k
1
vote
1
answer
271
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Physical interpretation of power law cluster size distribution in percolation problem
In the site percolation problem, when the occupation probability $p \rightarrow p_c$, where $p_c$ is the critical probability. The characteristic length diverges, and assuming the usual scaling ansatz ...
- 1,057
1
vote
0
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Reference: Renormalization Group and scale invariance in statistical mechanics [duplicate]
Can anyone recommend a book/resource that succinctly explains how the Renormalization Group idea is applied in statistical mechanics?
I have some background in undergraduate-level statmech, but none ...
14
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3
answers
6k
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Why correlation length diverges at critical point?
I want to ask about the behavior near critical point.
Let me take an example of ferromagnet.
At $T < T_c$, all spins are aligned to the same direction thus it is in the ordered state, scale ...
- 327
32
votes
2
answers
5k
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What is the difference between scale invariance and self-similarity?
I always thought that these two terms are some kind of synonyms, meaning that if you have a self-similar or scale invariant system, you can zoom in or out as you like and you will always see the same ...
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12
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6
answers
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Are the physical laws scale-dependent?
If you read the article "More Is Different", by P.W. Anderson (Science, 4 August 1972), you will find a deep question: are the physical laws dependent of the size of the system under study?
As an ...
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