The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.
15
votes
0answers
105 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The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
9
votes
0answers
53 views
Fluctuations of an interface with hammock potential
This question is related to that one. I ask it here since comments are too short for the extended discussion that was going on there.
I am interested in a very simple interface model. To each ...
8
votes
0answers
146 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 ...
7
votes
0answers
98 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
163 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 = ...
7
votes
0answers
53 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 ...
6
votes
0answers
64 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) ...
6
votes
0answers
39 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 ...
5
votes
0answers
52 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 ...
5
votes
0answers
254 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(Colloquium: Photons and electrons as emergent phenomena, Levin and Wen, Rev. Mod. Phys. 77, 871(2005), see e.g. http://arxiv.org/abs/cond-mat/0407140), ...
5
votes
0answers
170 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 ...
5
votes
0answers
212 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
128 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
72 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 ...
4
votes
0answers
67 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 ...
4
votes
0answers
112 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$$
...
4
votes
0answers
235 views
Relating the variance of the current operator to measurements
(EDIT: Thanks to Nathaniel's comments, I have altered the question to reflect the bits that I am still confused about.)
This is a general conceptual question, but for definiteness' sake, imagine a ...
4
votes
0answers
86 views
What is the proper time used in relativistic non equilibrium statistical physics?
In the literature one often finds covariant relativistic generalizations of classical non equilibrium statistical equations (Boltzmann, Vlasov, Landau, fokker-planck, etc...) but I wonder what is the ...
4
votes
0answers
57 views
Deviation from power law distribution of earthquakes
One of the most accepted framework on the relation between magnitude and frequency of the earthquakes, is that of the critical phenomena. In this framework magnitude of events must be distributed ...
3
votes
0answers
27 views
Lattice model completely constrained by boundary data
I am dealing with a lattice model that has the peculiar property that if I specify all the spins on the boundary, by local conservation laws, the whole lattice configuration (throughout the whole ...
3
votes
0answers
73 views
Spontaneous conversion of heat into work at negative temperatures
Consider a heavy macroscopic object moving in a gas. Friction causes its kinetic energy to be converted into heat. Thermodynamically, there is (effectively) no entropy associated with the kinetic ...
3
votes
0answers
70 views
Semi-conductors
Suppose there is a semiconductor with Fermi energy $E_f$ and that there are $N$ bound electron states.
I'd like to know why the mean number of excited electrons takes the form $$\bar n={N\over ...
3
votes
0answers
59 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
$$-\beta[f]=\lim_{n\to0}\{\frac{-\beta^2J^2}{4n}\sum_{a\ne b}q_{\alpha\beta}^2-\frac{\beta ...
3
votes
0answers
83 views
Qualitative argument to determine energy of defects
In a book of "LES HOUCHES - Critical Phenomena, Random systems, Gauge theories" the author Frolich says that:
2D
In two dimensions, the mean energy of an isolated point defect in a square area of ...
3
votes
0answers
123 views
Stability of the vacuum state of interacting quantum fields
"Stability" is generally taken to be the justification for requiring that the spectrum of the Hamiltonian should be bounded below. The spectrum of the Hamiltonian is not bounded below for thermal ...
3
votes
0answers
451 views
How do I derive the critical temperature for bose condensation in two dimensions?
In class we derived the 3D case, but there's a step I don't understand:
$$ 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 = ...
2
votes
0answers
39 views
What is the minimum non-integer dimension for which the XY model shows a phase transition? (if well-defined)
I know that XY statistical model for $d=2$ doesn't show a regular phase transition , while the $3d$ has, I was wondering what is the behaviour for $2< d < 3$.
If it is simpler one could ...
2
votes
0answers
63 views
Ising Hamiltonian for relativistic particles
An Ising system is described by the simple Hamiltonian:
$$H = \sum\limits_{i} c_{1i} x_{i} + \sum\limits_{i,j} c_{2ij} x_i x_j \,\,\,\,\,\,\,\,\,\,(1)$$
Here the $x_i$ are spins (+1 or -1 in units ...
2
votes
0answers
28 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 ...
2
votes
0answers
156 views
Pauli paramagnetism for electrons with external magnetic field
Apparently it is to be shown that for electrons under an external magnetic field, in the limit as $B\to 0 $
$$
\chi = \frac{dM}{dB} \approx \frac{n\,\mu^{*^2}}{k\,T}\,\frac{f_{1/2}(z)}{f_{3/2}(z)}
$$
...
2
votes
0answers
80 views
Deriving the “total” Bose Einstein density of states, including the condensate
Is is possible to derive the Bose-Einstein density of states containing the delta function representing the BE condensate?
2
votes
0answers
52 views
Spontaneous symmetry breaking in the quantum 1D XX model?
The ground states of the quantum 1D Ising and Heisenberg models exhibit spontaneous magnetization. Is this also true for the 1D XX model?
2
votes
0answers
138 views
Classical blackbody radiation 'solution'
I never understood how the equipartition theorem was applied electromagnetic waves inside the metallic blackbody. As hyperphysics puts it ...
2
votes
0answers
81 views
Why is the free energy minimized by the Boltzmann distribution?
Can someone show me, without glossing over anything, why $F = E - TS$ is minimized when $p_i = e^{-U_i/k_bT}/\sum_ie^{-U_i/k_bT}$? I understand it conceptually, but am having difficulty showing it ...
2
votes
0answers
53 views
Spin Glass Transitions in Random Bond Ising Model (RBIM)
In brief, is there a list of spin glass transition properties for the RBIM on different lattices? Is there any know results about the relationships between these probabilities for a graph and its ...
2
votes
0answers
47 views
Semiflexible discrete polymer chain
Suppose we have a 2D polymer model described by a set of 2D vectors {$\mathbf{t}_i$} ($i=1,2,\dots N$) of length $a$.
The energy of the polymer is given by:
$$
...
2
votes
0answers
99 views
Nonpertubative renormalization in quantum field theory versus statistical physics
I am trying to work my head around how renormalization works for quantum field theory. Most treatments cover perturbative renormalization theory and I am fine with this approach. But it is not the ...
2
votes
0answers
76 views
Stat mech explanation for separation of one liquid from another in gravity?
If one mixes two distinct ideal gases above the Earth's surface, one with a higher molecular mass than the other, then at equilibrium, their number density gradients will be such that at low heights, ...
2
votes
0answers
69 views
Randomly sampling a “well-mixed” solution of Brownian particles
I place $N$ Brownian particles in $V$ liters of solution, shake until I assume that the particles are "well-mixed", and sample and randomly sample an $S$ liter volume. What is the probability ...
2
votes
0answers
72 views
Factorization of fermionic scattering integral in 2d momentum rep
the scattering integrals for fermions involves both momentum ($k$) and energy ($k^2$) conservation and a nonlinear phase space factor of a distribution function $f(k)$.
$$\begin{multline}I(k) = ...
2
votes
0answers
186 views
How is the “negative dispersion” derived?
I'm looking at Kopfermann H., Ladenburg R., Nature, 122, 338-339 (1928) and it appears Ladenburg in Ladenburg R., Z.Physik, 4, 451-468 (1921) was the first to discover the phenomenon of "negative ...
1
vote
0answers
29 views
Calculating the change in entropy in a melting process
I have a homework question that I'm completely stumped on and need help solving it.
I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
1
vote
0answers
29 views
Neutron scattering for a critical magnetic-ordering system : what about critical opalescence?
Liquid-gas transition critical point is believed to share the same universality class as the 3D Ising model.
We know that the liquid-gas transition is characterized by a phenomenon called critical ...
1
vote
0answers
26 views
Is there anything to prevent paired-up neutrons from a complete overlap
The reason "neutrons don't overlap", as DarenW explained it, has to do with intricate forces at play that take into account the spins, iso-spins and symmetry of the wavefunctions.
However, assume I ...
1
vote
0answers
77 views
Rotational Constant and Moment of Inertia of Fluorine gas
I have come across some homework question on thermodynamics which needs me to calculate $B$ of $F_2$
My attempt:
$B= \frac{h}{8\pi^2cI}$ where $I=\mu r^2=\frac{m_1m_2}{m_1+m_2} r^2$
Atomic mass of ...
1
vote
0answers
44 views
Reaction coordinate as a function of atomic positions
I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM).
As a quick backdrop WHAM is a method for stitching ...
1
vote
0answers
57 views
Partition function for multidimensional scaling energy
Let $D_{ij}$ a random matrix with i.i.d positive coefficients. One can take for instance $D_{ij}$ uniformly distributed in [0,1]. We consider the following energy function $H(x)$ defined for ...
1
vote
0answers
73 views
Statistical Mechanic
One can define entropy as $$S=k\log{\omega(E)},$$ where $\omega(E)$ is the numbers of states with energy equal $E$; and the canonical partition function for a set of N particles is defined ...
1
vote
0answers
90 views
helmholtz free energy of a polymer
You have a polymer chain of $N$ units, which is represented by $N$ independent springs in series. The springs are Hookean, with spring constant $L$, and the end to end vector is $\mathbf r$. So the ...
1
vote
0answers
115 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 ...
