The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.

learn more… | top users | synonyms

26
votes
0answers
275 views

Systematic approach to deriving equations of collective field theory to any order

The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
15
votes
0answers
350 views

Can Lee-Yang zeros theorem account for triple point phase transition?

Now the prominent Lee-Yang theorem (or Physical Review 87, 410, 1952) has almost become a standard ingredient of any comprehensive statistical mechanics textbook. If the volume tends to infinity, ...
10
votes
0answers
194 views

List of known universality classes

I am working with RG and have a pretty good idea of how it works. However I have noticed that even though the idea of universality class is very general and makes it possible to classify critical ...
10
votes
0answers
85 views

Quantum statistics of branes

Quantum statistics of particles (bosons, fermions, anyons) arises due to the possible topologies of curves in D-dimensional spacetime winding around each other What happens if we replace particles by ...
8
votes
0answers
149 views

Measure of Lee-Yang zeros

Consider a statistical mechanical system (say the 1D Ising model) on a finite lattice of size $N$, and call the corresponding partition function (as a function of, say, real temperature and real ...
7
votes
0answers
81 views

Mean-field theory : variational approach versus self-consistency

I have a general question concerning mean-field approaches for condensed matter classical of quantum statistical mechanic systems. Does determining the mean-field by a variational approach always ...
7
votes
0answers
146 views

Diffusion of gases in the atmosphere

Suppose that the atmosphere is composed of 21% $O_2$ and 78% $Kr$ (instead of $N_2$). Since the density of $Kr$ is greater than the density of $O_2$, the lower atmosphere (where we live) should be ...
7
votes
0answers
104 views

Does quark color contribute to “spin degeneracy” for QGP calculations?

Like the title say, does quark color matter in counting contributions in a early universe plasma (QGP), as when adding up the total plasma energy density, or is it just spin? The book I have (Pathria) ...
7
votes
0answers
328 views

Is the “particle number” of “electrons” well defined in Wen's string-net theory of elementary particles?

According to professor Wen's string-net theory, electrons can be viewed as the elementary excitations of string-net objects. Just like the phonons and magnons are the elementary excitations of ...
7
votes
0answers
69 views

Do bipartite spin glasses have simple relaxation dynamics?

From what I gather, a Boltzmann machine (BM) is essentially a spin glass with no applied field evolving under Glauber dynamics (if this is at all mistaken, I don't think it will be off enough to ...
7
votes
0answers
290 views

Information geometry of 1D Ising model in complex magnetic field regime

Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by $$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
6
votes
0answers
129 views

2d Ising model in CFT and statistical mechanics

When I recently started to read about conformal field theory, one of the basic examples there is the so called Ising model. It is characterized by certain specific collection of fields on the plane ...
6
votes
0answers
89 views

Does the Standard Model plasma develop a spontaneous magnetisation at finite temperature?

Reference: arXiv:1204.3604v1 [hep-ph] Long-range magnetic fields in the ground state of the Standard Model plasma. Alexey Boyarsky, Oleg Ruchayskiy, Mikhail Shaposhnikov. The authors of this paper ...
6
votes
0answers
193 views

Drawing the RG flow diagram

In real-space renormalization group how does one find the complete RG flow exactly, (not schematically)? I understand it needs to be done on a computer. For example, I have the ising model on a ...
6
votes
0answers
196 views

Are there known turbulent nonlinear equations where the cascade is a thermal gradient?

In a recent answer (here: The equipartition theorem in momentum space ), I suggested that if you have an appropriate first order equation (in the answer I used a second order equation, but it is more ...
6
votes
0answers
273 views

Tsallis entropy and other generalizations

If I am given a system, which I might have to describe using a generalized entropy, like the "q-deformed" Tsallis entropy, do I have to fit q from experiment or might I know it beforehand? How do I ...
5
votes
0answers
127 views

Fluctuation interaction between two uncharged spheres

I'm trying to figure out quantitatively what is the force, acting between two uncharged conducting spheres and I've got stuck. It is not a kind of homework - it is just a simple act of curiosity. I'd ...
5
votes
0answers
191 views

Duality between Euclidean time and finite temperature, QFT and quantum gravity, and AdS/CFT

The thoughts below have occurred to me, several years ago (since 200x), again and again, since I learn quantum field theory(QFT) and statistical mechanics, and later AdS/CFT. It is about the duality ...
5
votes
0answers
70 views

Some questions about the large-N Gross-Neveu-Yukawa model

Consider the following action with a fermionic field $\psi$ and a scalar field $\sigma$, $S = \int d^dx \{ -\bar{\psi}(\gamma^\mu \partial_\mu +\sigma )\psi + \Lambda^{d-4}[ \frac{(\partial_\mu ...
5
votes
0answers
159 views

What is the physical interpretation of the Papadodimas/Raju mirror operators?

In this paper http://arxiv.org/abs/1310.6335, the authors discuss the firewall problem and contruct so called mirror operators appearing in the correlation function. The key part seems to be (2.6) ...
5
votes
0answers
468 views

Is Feynman talking about the Zeroth Law of Thermodynamics?

In Volume 1 Chapter 39 of the Feynman Lectures on Physics, Feynman derives the ideal gas law from Newton's laws of motion. But then on page 41-1, he puts a caveat to the derivation he has just ...
5
votes
0answers
100 views

Exact Beta Functions in Statistical Mechanics

I'm looking for analytically solvable models in statistical mechanics (classical or quantum) or related areas such as solid state physics in which the beta function for a certain renormalization ...
5
votes
0answers
112 views

What is the proper time used in relativistic non equilibrium statistical physics?

In the literature one often finds covariant relativistic generalizations of classical non equilibrium statistical equations (Boltzmann, Vlasov, Landau, fokker-planck, etc...) but I wonder what is the ...
5
votes
0answers
153 views

Applicability of Baxter's method for IRF models

In a interaction-round-a-face model of $n^2$ particles in a lattice, a weight $W(a,b,c,d)$ is assigned to each face in the lattice based on the spins $a,b,c,d$ (listed say from the bottom-left corner ...
4
votes
0answers
69 views

References to Mechanics (Classical, Quantum, Statistical) using Time-Scale calculus?

Time-Scale Calculus, is a theory which unifies ordinary (plus fractional and q-) calculus with discrete (and finite differences) calculus. In a sense, in a similar way the Lebesgue integral (or ...
4
votes
0answers
65 views

Is the stability matrix of a linearised RG flow always diagonalisable?

This is a follow up on "Why are the eigenvalues of a linearized RG transformation real?". My question is simple: Is there some physical (or mathematical) reason for the stability matrix of ...
4
votes
0answers
57 views

Help with deriving an asymptotic expression

Note: I don't know if this is the best place for this question, because it is very specific. However, I'm not sure of a better place to go (apart from one of the other SE's). If you have a ...
4
votes
0answers
87 views

Wilson's Renormalization Group and Lie's Third Theorem

If you think of a one-parameter group of transformations along a curve in the plane as a (Lie) group, and the tangent vector to the curve as a generator of the curve we can intuitively understand ...
4
votes
0answers
73 views

Intuitively, why does removing solutes cost $k_B T$ of free energy per molecule?

I can calculate that if you want to, for example, desalinate water, you will have to pay a free energy cost of $k_B T$ for each ion you remove. In other words, removing an ion from a volume of water ...
4
votes
0answers
72 views

(Euclideanized) QFT on $S^d$ vs $S^{d-1}\times S^1$

Broadly I would like to understand what is the difference in the physical interpretation of a (Euclideanized) QFT which is on space-time $S^d$ and which is on a space-time $S^{d-1}\times S^1$. In ...
4
votes
0answers
86 views

Free path distribution

I'm studying statistical mechanics, and I'm trying to resolve some problem known from my thermodynamics course. So I want to calculate mean free path for particles with a concentration $n$ and ...
4
votes
0answers
80 views

Can the correlation for the Potts model be bounded?

I am studying a $d$-state Potts model. A configuration $\sigma$, which assigns for each $x\in \mathbb{Z}^2$ a value $\sigma(x)\in [1,2,\ldots,d]$, with the probability on a finite lattice defined as ...
4
votes
0answers
103 views

Cauchy Problem for Boltzmann Equations

One of the first profound analysis about the solutions of the Boltzmann Equation was given by DiPerna and Lions in the late 1980s. You can find one of their main papers here: ...
4
votes
0answers
136 views

Lattice model completely constrained by boundary data

I am dealing with a lattice model that has the peculiar property that if I specify all the spins on the boundary, by local conservation laws, the whole lattice configuration (throughout the whole ...
4
votes
0answers
140 views

Thermal equilibrium and non correlations

I read in a book on quantum fluctuations and quantum noise that, at thermal equilibrium the classical canonical variables are uncorrelated, ie: $$\langle xp\rangle=\langle x\rangle\langle p\rangle$$ ...
4
votes
0answers
287 views

Stability of the vacuum state of interacting quantum fields

"Stability" is generally taken to be the justification for requiring that the spectrum of the Hamiltonian should be bounded below. The spectrum of the Hamiltonian is not bounded below for thermal ...
3
votes
0answers
50 views

Partition function of classical quadrupole in an electric field

The partition function of a dipole in an electric field is a well-known problem, analytical solvable (nice integral, can be calculated with pen and paper), for example in the Langevin treatment of ...
3
votes
0answers
90 views

Why is there a 'loophole' in Mermin Wagner for rotations?

I'm just starting out in my mathematics career by looking at some simple stuff on broken symmetries in statistical mechanics. Since 3D is 'hard' it would be very nice to look at 2D toy models of ...
3
votes
0answers
45 views

Is there a general H-theorem?

In statistical mechanics, Boltzmann showed that for dilute gases the H-function increases. I remember from a lecture that there is no general H-theorem, e.g. for non-dilute gases or in the quantum ...
3
votes
0answers
80 views

Critical temperature difference between Ising and XY model

The following formula gives the critical coupling (more precisely the ratio of the spin-spin coupling over the temperature) for $O(n)$ models on a triangular lattice: ...
3
votes
0answers
69 views

What real experimental systems are well-described by Glauber-Ising spins?

I'm hoping for references to actual physical systems in which all or at least most of the following can be simultaneously characterized: the spin flip rate, the temperature, and a relaxation or ...
3
votes
0answers
576 views

Numerical problem in solving the Bogoliubov de Gennes equations- methods to solve?

I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} ...
3
votes
0answers
58 views

Infinite quon statistics/Quantum Boltzmann statistics: models and hamiltonians

I learned long ago that there are some exotic classes of statistics. One of them is calleq $q$-on or quon statistics. It is given by $$a_ia^+_j-qa^+_ja_i=\delta_{ij}$$ Infinite statistics (Quantum ...
3
votes
0answers
63 views

Where else in physics does one encounter Reynolds averaging?

Reynolds-averaged Navier–Stokes equations (RANS) is one of the approaches to turbulence description. Physical quantities, like for example velocity $u_i$, are represented as a sum of a mean and a ...
3
votes
0answers
140 views

Impact of the noise distribution on Geometric Brownian motion

I have a problem which includes geometric Brownian motion, with either normally distributed or power-law-distributed noise, and I'm asking for some explanations and if possible references to read in ...
3
votes
0answers
99 views

Evolution of black holes ensemble

Background: I’ve read many times that arrow of time can be explained from extremely low entropy of the Universe at the Big Bang (http://preposterousuniverse.com/eternitytohere/faq.html). The argument ...
3
votes
0answers
98 views

Monte Carlo for Random Bond Ising ferromagnet

The set-up: Consider the Ising model on an $L \times L$ square lattice, where the coupling of each bond is chosen to be $+J$ (ferromagnetic) with probability $(1-p)$ and $-J$ (antiferromagnetic) with ...
3
votes
0answers
67 views

Question about the derivation of an equation in full replica symmetry breaking solution

Using replica method and saddle point method, the free energy of a magnetic system can be expressed as $$-\beta[f]=\lim_{n\to0}\{\frac{-\beta^2J^2}{4n}\sum_{a\ne b}q_{\alpha\beta}^2-\frac{\beta ...
3
votes
0answers
110 views

Qualitative argument to determine energy of defects

In a book of "LES HOUCHES - Critical Phenomena, Random systems, Gauge theories" the author Frolich says that: 2D In two dimensions, the mean energy of an isolated point defect in a square area of ...
3
votes
0answers
685 views

How do I derive the critical temperature for bose condensation in two dimensions?

In class we derived the 3D case, but there's a step I don't understand: $$ N = g \cdot {V \over (2 \pi \hbar)^3} \cdot \int\limits_{0}^{\infty}{1 \over{e^{\left( E_p \over{K_B T}\right)}-1}} d^3 p = ...