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Questions tagged [statistical-mechanics]

The study of large, complicated systems by means of statistics and probability theory, in order to extract average properties and to provide a connection between mechanics and thermodynamics.

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948 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The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
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1k 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, ...
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944 views

Intuition for when the replica trick should work and why it works

I am a graduate student in mathematics working in probability (without a very good background in physics honestly) and I've started to see arguments based on computations derived from the replica ...
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200 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 ...
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247 views

Renormalisation and the Fisher-Rao metric

The renormalisation group (I'm talking about classical, statistical physics here, I'm not familiar with field theory too much) can be though of as a flux in a space of possible Hamiltonians for a ...
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435 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 ...
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267 views

Are there classical infinite order / continuous non-symmetry breaking phase transititions besides BKT?

At the Berezinskii-Kosterlitz-Thouless (BKT) phase transition, the singular part of the free energy behaves as $\xi^{-2}$, where $\xi \propto e^{c/\sqrt{T-T_c}}$ (with $c>0$) is the correlation ...
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255 views

Absence of phase transitions in quantum 1D systems at positive temperature

While it is generally said that there are no phase transitions in classical lattice systems in one spatial dimension, there are also exceptions to this rule. Rigorous proofs involve some fairly strong ...
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139 views

What are good books covering information theoretic approaches to theoretical physics?

I am about to finish my undergraduate studies and am very interested in going into the applications of information theory to either general relativity, or quantum mechanics. However I have been ...
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187 views

Phil Anderson's Criticism of Existence of Stable Dissipative Structures

In this book chapter (1987), titled "Broken symmetry, emergent properties, dissipative structures, life," Phil Anderson and Daniel Stein criticize defining life as a dissipative structure (a ...
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160 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) ...
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128 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 ...
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401 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 ...
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469 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 ...
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143 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 ...
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593 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 ...
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489 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 = ...
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82 views

Entropy and equilibrium concepts at astronomic scales

I am always puzzled to read here and there discussions dealing with thermodynamic concepts applied to astronomic scales where gravity matters. To my opinion, there is a certain carelessness to go into ...
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153 views

Physical examples of log CFTs

There are examples of CFTs having correlators with logarithms. What are the examples of physical systems exhibiting such logarithmic behaviour (particularly in $d>2$ dimensions)?
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324 views

Free Energy Landscape - Construction and meaning?

I struggle to understand the concept of free-energy landscape. It seems to me the concept makes perfect sense for energies, but not for (canonical) free energies. In my actual, hopefully to be ...
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339 views

Relationship between the statistical mechanics partition function and the path integral correlation function

In the path integral formulation I have $Z[J]$, the generating functional of correlation functions, and $W[J]=\frac{i}{\hbar} \ln{Z[J]}$, the generating functional of connected correlation functions. ...
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83 views

Is there any useful sense in which entropy fluctuates?

One of the classic distinctions between young Boltzmann and old Boltzmann was his view on entropy. Young Boltzmann had his H-theorem where a mechanical quantity H was supposed to represent entropy. ...
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347 views

Nose-Hoover Barostat

Much can be found about the Nose-Hoover Thermostat. However I seem to be having difficulty finding out details about the Nose-Hoover Barostat, and how it is implemented. Would anyone be able to give ...
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324 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) ...
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254 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 ...
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252 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 ...
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40 views

What are the excitations in the near critical 2D-Ising model in a magnetic field?

Apparently it is well known that the 2D Ising model with $T=T_C$ in a small magnetic field has a mass gap and correlation length $\xi \sim h^{- \frac{8}{15}} $. Further, in a paper in 1989 ...
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56 views

Bose Condensation; interacting vs. non-interacting

I have some problems unifying, the two way I learned how a Bose condensate appears. The main problem is that the observables seem to be quite different. In statistical physics lecture one starts with ...
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91 views

Do systems of fermions take longer to equilibrate than systems of bosons for complexity-theoretic reasons?

This excellent paper by Scott Aaronson persuasively argues that computational complexity can be relevant for physical processes. In particular, what's hard for a hypothetical Turing machine to do may ...
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166 views

Is it possible to derive Liouville's Theorem purely from maximum differential entropy?

Typically in physics (at least the way I learned mechanics), this is derived using the multi-dimensional divergence theorem on the $2N$-dimensional phase space i.e. $0=\partial_t \rho + \sum\limits_{...
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76 views

Do exactly solvable stat mech systems admit efficient algorithms for finite sizes?

I come from a background in statistical mechanics (not algorithm design or complexity theory), and the following question occurred to me that I could use some expert help in beginning to understand. ...
5
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0answers
211 views

Violations of Onsager reciprocity?

As far as I understand it, the modern statement of Onsager reciprocity is that the linear-response transport coefficient matrix, when transposed, is equal to that of the time-reversed system (reversed ...
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272 views

Fluctuation-dissipation theorem and Kramers-Kronig relations

Is there any connection between fluctuation dissipation theorem and Kramers-Kronig relations? They are often described together under "Linear response theory" but I do not see any exact connection (...
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302 views

Thermodynamic equilibrium or thermal equilibrium and equipartition theorem

In all derivations of the equipartition theorem I can find a thermodynamic equilibrium distribution is used to show it's validity. But more vague sources (physics.stackexchange answer by Luboš Motl, ...
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161 views

on fundamental 2D conductivity equation boundary value problem

Consider the following homogeneous boundary value problem for a function/potential $u(x,y)$ on the infinite strip $[-\infty,\infty]\times[0,\pi/4]$ w/positive periodic coefficient/nductivity $\gamma(x+...
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890 views

Adiabatic invariant and Liouville's theorem

It appears that many people have tried to show adiabatic theorem from Liouville's theorem, e.g., Li's note, or at least tried to find some relations, e.g., Rugh, Adib and Tong's lecture notes Sec. 4.6....
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218 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 \...
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436 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 ...
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0answers
126 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 ...
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148 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 ...
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0answers
1k views

An explanation for the Landauer's principle

Has anyone understood the Landauer's principle? What is the current status? In specific, is there a theoretical derivation of the Landauer's Principle?(not the heuristic one based on Salizard's ...
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0answers
220 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 ...
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44 views

What happens to topological insulators at finite temperature?

There is a similar question here, but I had a few things I wanted to ask. So basically pretty much all analysis/ theory of topological insulators is for pure wave-functions and conservative ...
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0answers
72 views

How does renormalization relate to emergence?

In statistical mechanics renormalization is often related to coarse-graining which in turn allows to calculate some macroscopic states. The resulting macroscopic description is sometimes called ...
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0answers
92 views

Weird and unintuitive results from thermodynamics/hydrostatics for an isothermal atmosphere and possible explanation(?)

It is known from hydrostatics that for a fluid in equilibrium in a gravitational field, $$\frac{dP}{dz} = -ρg$$ Let us from now on suppose the atmosphere is isothermal and has temperature $T$. We ...
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0answers
146 views

What are some good articles on trend to equilibrium?

I am interested in studying systems out of equilibrium that are trending to equilibrium. Trend to equilibrium, entropy production, etc. seem to be very tricky topics. Any suggestions will be ...
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159 views

Is there any example of a real-life system which violates the “third law” of thermodynamics while remaining at equilibrium?

I assume the following statement for the "third law" of thermodynamics: $$\lim_{N \to \infty} \lim_{T \to 0} \frac{S}{N} = 0 \tag{1}\label{1}$$ That is to say, I am considering those systems with a ...
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56 views

Validity of Boltzmanns Equation and $H$-function theorem?

A while ago I came across a resource (which I have forgotten) on the validity of Boltzmann's equation. It talked about the fact that the Boltzmann's equation is valid at the extrema of the $H$-...
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0answers
421 views

Entropy of a Bose-Einstein condensate

I would like to understand why Bose-Einstein condensation can occur only for $d>2$ dimensions. Therefore, I want to know what the entropy of a Bose-Einstein condensate is. The grand canonical ...
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0answers
118 views

What's the meaning of chemical potential of photons or phonons?

The chemical potential of photons or phonons vanishes due to their particle number not conserved, I don't understand it very well. So can you expain what's the meaning of chemical potential of them ...