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Results tagged with statistical-physics
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user 150264
The study of physical systems using probabilistic reasoning, especially relating small-scale classical mechanics to large-scale thermodynamics.
1
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answer
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What is the definition of the thermodynamic limit of a thermodynamic quantity?
Statistical mechanics is all about taking thermodynamic limits and, as far as I know, there are more than one way to define such limits. Consider the following theorem:
Theorem: In the thermodynamic l …
- 3,535
0
votes
0
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85
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Sine-Gordon transformation and functional integrals
In the past months, I've been trying to understand the so-called Sine-Gordon transformation, so I've posted some questions here about this topic. I also did an extensive research about this subject, s …
- 3,535
5
votes
1
answer
392
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Renormalization group strategies
Before introducing block spin transformations in chapter four of Random Walks, Critical Phenomena and Triviality in Quantum Field Theory, the authors state the following:
"In this chapter we sketc …
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5
votes
1
answer
430
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Effective action, partition function and the renormalization group
Mayer expansions and the Hamilton–Jacobi equation by D. Brydges and T. Kennedy begins mentioning that many problems in statistical mechanics and QFT center on the analysis of integrals of the form:
\b …
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4
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2
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467
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Path integrals on statistical mechanics
In (rigorous) statistical mechanics and statistical field theory one is usually concerned in giving meaning to integrals of the form:
\begin{eqnarray}
\langle \mathcal{O}\rangle = \frac{1}{Z}\int D\ph …
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2
votes
2
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427
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What's the current state of cluster expansions?
A classic reference on cluster expansions in mathematical physics (specially statistical mechanics) is these lecture notes by professor Brydges for a les Houches course in 1984 on the mentioned topic. …
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392
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Is there a general theory for Wilsonian renormalization?
I know that Wilson's renormalization group is not a theory per se and that there are many ways to implement it in a given system. Also, renormalization group techniques are applied in a large number o …
- 3,535
14
votes
2
answers
941
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How are Clifford algebras and spinors used to study the Ising model?
I've heard Clifford algebras and spinors are useful tools to study the Ising model, but I've never find any good discussion on this matter. Also, as far as I know, in the original solutions of the 2-D …
- 3,535
3
votes
1
answer
223
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Mathematical meaning for the (continuous) Sine-Gordon transformation
I've been trying to understand the so-called Sine-Gordon Transformation which occurs in both classical and quantum statistical mechanics. One of the most cited references on this topic seems to be Frö …
- 3,535
8
votes
1
answer
211
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From the conceptual idea of the RG to its actual implementation
Everytime I want to understand a little more about the ideas behind Renormalization Group techniques, I get troubled by a gap between the general picture one usually presents (e.g. in books or pedagog …
- 3,535
2
votes
2
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290
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Imprecise Definition of a $\sigma$-algebra
I'm reading some works on the hierarchical model in statistical mechanics and I came across an strange definition, which I need to clarify. Consider a finite set $\Lambda \subset \mathbb{Z}^{d}$. The …
- 3,535
2
votes
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answer
234
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Thermodynamic limit and Gaussian measures
Let $\Lambda \subset \mathbb{Z}^{d}$ be finite and fixed and consider $\mathbb{R}^{|\Lambda|}$ be the vector space of all sequences $\varphi = (\varphi_{x})_{x\in \Lambda}$. We equip $\mathbb{R}^{|\La …
- 3,535
5
votes
1
answer
355
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How can one recover/obtain information from the renormalization group procedure?
I know the basic idea behind the renormalization group approach as it is used in mathematical physics to study both QFT and statistical mechanics. However, I have trouble understanding how can one rec …
- 3,535
5
votes
1
answer
519
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Reference Request for a particular approach of (rigorous) statistical mechanics
I was reading Mathematical Aspects of Quantum Field Theory by. E. de Faria and W. de Melo, and the following caught my attention.
In (Hamiltonian) mechanics, the states of a system are described by p …
- 3,535
6
votes
2
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639
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Explicit form of this unitary transformation
Disclaimer: This question has its motivation from physics. It is probably not entirely rigorous at the moment. I just want to clarify some steps and try to make the arguments rigorous afterwards, if p …
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