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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47
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960 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The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...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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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 ...
22
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1answer
689 views

How is the logarithmic correction to the entropy of a non extremal black hole derived?

I`ve just read, that for non extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that $S = \frac{A}{4G} + K ...
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206 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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259 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 ...
14
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446 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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286 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 ...
12
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1answer
347 views

Why are superfluid vortex lattices stable?

Both (a) neutral superfluids that are externally rotated, and (b) type-II superconductors (i.e. charged superfluids) under applied magnetic fields between the critical fields $h_{c1}$ and $h_{c2}$, ...
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154 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 ...
9
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296 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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265 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 ...
8
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1answer
312 views

Computational scaling of quantum and classical Monte Carlo algorithms

How does the computational complexity of finding an equilibrium thermal state for a given Hamiltonian at a given temperature scale with system size under classical and quantum Monte Carlo? I know ...
8
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1answer
593 views

Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
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165 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) ...
8
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129 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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402 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 ...
8
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482 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 ...
8
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144 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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91 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 ...
7
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2answers
345 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf j_{\...
7
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505 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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598 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 ...
6
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2answers
138 views

How do you measure the chemical potential?

It is clear how to measure thermodynamics quantities such as temperature, pressure, energy, particle number and volume. But I have no idea how to measure chemical potential. Could someone please ...
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155 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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342 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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373 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. ...
6
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1answer
181 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_{...
6
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365 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 ...
6
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332 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) ...
6
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4answers
893 views

Distinguishable, indistinguishable paramagnetic ideal gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
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258 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 ...
6
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0answers
253 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
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2answers
248 views

Do unstable equilibria lead to a violation of Liouville's theorem?

Liouville's theorem says that the flow in phase space is like an incompressible fluid. One implication of this is that if two systems start at different points in phase space their phase-space ...
6
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1answer
395 views

Calculate the entropy per atom in Bohmian Mechanics

Bohmian mechanics description of a large number of interacting atoms would require a large phase space due to the large number of classical degrees of freedom. The entropy per atom is given as the ...
6
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2answers
2k views

Bose-Einstein condensation and phase transition

I would like to ask the following question for which I cannot find a definite answer in the literature. Of what ORDER is the phase transition leading to Bose-Einstein condensation for a ideal and ...
5
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65 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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81 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 ...
5
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58 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 ...
5
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0answers
93 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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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
224 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 ...
5
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0answers
281 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 (...
5
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0answers
310 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+...
5
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1answer
218 views

Proof of periodicity of Floquet Green's function

It is claimed in many papers that the two-time Green's function in time periodic Hamiltonian case is periodic in the average time, i.e. \begin{equation} G(t+T,t'+T)=G(t,t') \end{equation} when $H(t+...
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930 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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1answer
329 views

Thermodynamics, chaperones: How to model polymer fragmentation?

Living polymers are well described by equilibrium statistical physics. Now I would like to consider a case were living polymers undergo fragmentation due to chaperones. I can think of a kinetic ...
5
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0answers
223 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
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0answers
459 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 ...