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7
votes
2answers
371 views

Does there exist a potential which realizes this strange quantum mechanical system?

I have done some courses on quantum mechanics and statistical mechanics in the past. Since I also do math, I wonder about converge issues which are usually not such a problem in physics. One of those ...
4
votes
3answers
1k views

Statistical physics of string theory

Is there any connection between statistical physics and string theory, or a statistical interpretation of string theory, perhaps? I mean, the way electromagnetic forces and thermodynamic laws are ...
13
votes
5answers
1k views

Can I derive the Boltzmann distribution by an invariance argument?

In statistical mechanics, the Boltzmann distribution gives the probability of a system being in state $i$ as $$\displaystyle \frac{e^{- \beta E_i}}{\sum_i e^{-\beta E_i}}$$ where $E_i$ is the energy ...
2
votes
1answer
1k views

Mathematica/Matlab/other for calculating Onsager's exact solution to the 2d Ising model

Would anybody be able to share a Mathematica/Matlab/other script for calculating Onsager's exact solution for the magnetisation of the 2d Ising model? I would be most grateful of one in order to test ...
8
votes
5answers
557 views

Persistence of fixed points under perturbation in dynamical systems

Suppose we have a smooth dynamical system on $R^n$ (defined by a system of ODEs). Assuming that the system has a finite set of fixed points, I am interested in knowing (or obtaining references about) ...
6
votes
1answer
435 views

For which values of $N$ is known the Lieb-Simon Inequality for $Z_N$ Models ?

Background: Let $\mathbb Z^d$ denote the $d$-dimensional integer lattice with norm $|x|=\sum_i|x_i|$. For each $x\in\mathbb Z^d$ we associate a spin variable, $\sigma_x$ taking values on the set ...
1
vote
0answers
202 views

Learning statistical mechanics for non-particle phenomena

I'm interested in various areas of complex systems, and I often come across articles like these: http://arxiv.org/PS_cache/cond-mat/pdf/0106/0106096v1.pdf http://arxiv.org/abs/cond-mat/9804180 The ...
7
votes
1answer
231 views

Existence of Limiting Distribution for Moving Regions in Stat. Phys. Models

As the title (hopefully) suggests, I've been trying to prove (or disprove) the existence of a limiting distribution for a certain projection in a statistical physics model. I'll give the details of ...
3
votes
0answers
156 views

What is the underlying graphical calculus of the Interactions-Round-a-Face lattice model?

Background Let $\mathcal{L}$ be an $m \times n$ square lattice on a torus, and let $\Sigma$ be a finite set. We think of $\Sigma$ as the possible spin values that can be assigned to the points of the ...
1
vote
1answer
513 views

Entropy of Markov processes

Consider a Markov process $X_t$ with generator $L$ and invariant distribution $\pi$, whose distribution at time $t$ is given by $\pi(t,dx)=\phi(t,x) \pi(dx)$ - in other word, $\phi(t,x)$ is the ...
4
votes
2answers
534 views

Mathematical means of studying large and complex but finite systems?

I want a list of the sort of mathematics/mathematical tools that are applied to the study of complex and probabilistic systems in order to make quantitative and qualitative observations about their ...
17
votes
2answers
1k views

Why don't existence and uniqueness for the Boltzmann equation imply the same for Navier-Stokes?

As I understand it, Lions and DiPerna demonstrated existence and uniqueness for the Boltzmann equation. Moreover, this paper claims that Appropriately scaled families of DiPerna–Lions ...
12
votes
2answers
1k views

What (if anything) happened to Viennot's theory of Heaps of pieces?

In 1986 G.X. Viennot published "Heaps of pieces, I : Basic definitions and combinatorial lemmas" where he developed the theory of heaps of pieces, from the abstract: a geometric interpretation of ...
6
votes
2answers
286 views

Examples of Slowly Mixing Chains in Statistics

This should probably be community wiki, but I don't know how to set that myself. I'm looking for examples or Markov chains that are used in statistics or statistical physics, and which are known to ...
3
votes
0answers
179 views

What is known about first return times to Markov partitions for Anosov diffeomorphisms?

Consider an Anosov diffeomorphism $T: M \rightarrow M$ and a corresponding Markov partition $\mathcal{R}$ of $M$. For $x \in M$, let $\mathcal{R}(x)$ denote the element of $\mathcal{R}$ containing $x$ ...