# Questions tagged [statistical-physics]

The study of physical systems using probabilistic reasoning, especially relating small-scale classical mechanics to large-scale thermodynamics.

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### How do I solve this $\mu(T) \approx \mu_f \left( 1 - \frac{\pi^2 k_B^2 T^2}{12 \mu(t)} \right)$? [closed]

I'm trying to solve this equation in the context of the statistical physics and because I have to do a code that is able to return the value of $\mu(T)$ but because $\mu(T)$ is a function of itself I ...
1 vote
62 views

### Probabilistic 2D cellular automata with memory lifetime increasing like $e^{L^2}$

Consider 2-state probabilistic cellular automata on an $L\times L$ torus square lattice which has the all-$0$ and all-$1$ configurations as fixed points, thinking of something similar to Toom's rule ...
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### Limiting value of trace of resolvent matrix involving two independent Wishart random matrices

Let $n_1$, $n_2$, and $d$ be positive integers tending to infinity such that $$d/n_k \to \phi_k \in (0,\infty).$$ Let $X_1 \in \mathbb R^{n_1 \times d}$ and $X_2^{n_2 \times d}$ be independent ...
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555 views

### Algebra/Algebraic geometry in statistical mechanics

This is a soft question. I am currently studying statistical mechanics and I found this one by chance: Algebraic statistical mechanics And I also found some workshops on interactions between ...
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1 vote
59 views

### Under which condition, such that all second-order critical points satisfy $\sum_j\cos(\theta_i-\theta_j)>0$ for all $i\in[n]$?

Consider the following non-convex function $$E(\theta):=-\sum_{i,j}A_{ij}\cos(\theta_i-\theta_j)$$ where $A$ is a symmetric, diagonal-free matrix whose non-diagonal element are $\pm 1$. In other words,...
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1 vote
146 views

### Recommendation to understand mean field theorem

I am studying Rodnianski and Schlein - Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics. Everything was clear for me and I reproved everything before inequality (3.22) (except ...
• 159
437 views

### Why computing $n$-point correlations?

I am trying to find a sufficiently convincing answer to this question, but it has been taking so much of my time and I can't get anywhere. It also follows my previous question on PSE. In axiomatic QFT,...
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210 views

### Reference for rigorous interacting many-body quantum mechanics

Are there good references for (both zero and finite time) interacting systems of quantum many-body theory? More precisely, I would be interested in references discussing the following topics: Second ...
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1 vote
97 views

### Mixing for a gas of hard spheres

The gas of hard spheres is a model for a gas in a container, where each particle is a sphere of radius $\epsilon$. The spheres interact with each other and with the container with elastic collisions. ...
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129 views

### Overview resources for (rigorous) critical phenomena

I recently came across this overview which discusses some results in the theory of critical phenomena. It is already quite old and I would like to know if there are other (more recent) overviews in ...
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589 views

### Progress on Simon's 1984 problem of the proof of Universality

I am writing this post to inquire if any progress has been made in solving problem 8B (Proof of Universality) proposed by Barry Simon in 1984. The problem goes like this: Show that the critical ...
235 views

### $\log\det$ asymptotics of a skew-circulant matrix with additive diagonal bimodal disorder

I'd like to share a problem that I have been dealing with for a longer time now. In the framework of quenched disorder in the square-lattice Ising model I want to calculate, for large even $M$, the ...
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623 views

### 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 ...
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1 vote
55 views

### Limiting value of expectation of trace of truncated Gram matrix

Let $n$ and $d$ be large positive integers such that $d/n = a \in (0,1)$, fixed. Let $x_1,\ldots,x_n$ be iid random vectors from $N(0,I_d)$. Fix $b \in (0,1]$ and a unit-vector $v \in \mathbb R^d$, ...
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