# Tagged Questions

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

0answers
26 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 ...
1answer
58 views

### NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms

From the papers by Barahona and Istrail I understand that a combinatorial approach is followed to prove the NP-completeness of non-planar Ising models. Basic idea is non-planarity here. On the other ...
2answers
57 views

### Energy dependent Maxwell-Boltzmann distribution

I'm having a bit of a problem figuring out the energy dependent Maxwell-Boltzmann distribution. According to my book (Ashcroft & Mermin) they write the velocity dependent distribution as: ...
2answers
56 views

### What is the derivation for the exponential energy relation and where does it apply?

Very often when people state a relaxation time $\tau_\text{kin-kin}, \tau_\text{rot-kin}$,, etc. they think of a context where the energy relaxation goes as $\propto\text e^{-t/\tau}$. Related is an ...
3answers
161 views

### Definition of entropy

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) entropy of a variable $X$ is ...
0answers
38 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 ...
2answers
77 views

### What would happen if energy was conserved but phase space volume wasn't? (and vice-versa)

I'm trying to understand the relationship between the two conservation laws. As I understand, Liouville's result is a weaker condition: it relies merely on the particular form assumed by Hamilton's ...
4answers
84 views

### The Preference for Low Energy States

The idea that systems will achieve the lowest energy state they can because they are more "stable" is clear enough. My question is, what causes this tendency? I've researched the question and been ...
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 ...
4answers
187 views

### If particles can find themselves spontaneously arranged, isn't entropy actually decreasing?

Take a box of gas particles. At $t = 0$, the distribution of particles is homogeneous. There is a small probability that at $t = 1$, all particles go to the left side of the box. In this case, entropy ...
1answer
67 views

### What is the interface tension between ordered and disordered phases of the Potts model?

I read in these papers(1,2) the concept of interface tension. I can't understand its definition. I can hardly imagine there is some tension in a model. Any help will be appreciated.
1answer
40 views

### Temperature of a small system

What is wrong if I define temperature of a small system (I mean, a system which has not a large number of particles) by $$1/T = dS/dE$$ ?
1answer
117 views

### Phase space in quantum mechanics and Heisenberg uncertainty principle

In my book about quantum mechanics they give a derivation that for one particle an area of $h$ in $2D$ phase space contains exactly one quantum mechanical state. In my book about statistical physics ...
2answers
83 views

### Independent systems and Lagrangians

Definition 1: The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
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 ...
3answers
68 views

### Microscopic picture of an inductor

I have a good understanding of how inductors behave in electrical circuits, and a somewhat rough-and-ready understanding of how this behaviour arises from Maxwell's equations. However, what I don't ...
0answers
27 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 ...
3answers
223 views

### Is there a way to obtain the classical partition function from the quantum partition function in the limit $h \rightarrow 0$?

One would like to motivate the classical partition function in the following way: in the limit that the spacing between the energies (generally on the order of $h$) becomes small relative to the ...
0answers
39 views

### Lambda transition data points of $\require{mhchem}\ce{^4He}$

I'm looking to get some data on the lambda transition of $\require{mhchem}\ce{^4He}$. I need the data points of the specific heat vs. temperature graph, if that makes sense.
1answer
46 views

### Number of particles in a microcanonical ensemble

Is it always assumed that, in a microcanonical ensemble, the number of particles is $N \gg 1$ ? If no, are all the theorems related to the microcanonical description true even if the number of ...
3answers
287 views

### Why does the Boltzmann factor $e^{-E/kT}$ seem to imply that lower energies are more likely?

I'm looking for an intuitive understanding of the factor $$e^{-E/kT}$$ so often discussed. If we interpret this as a kind of probability distribution of phase space, so that \rho(E) = ...
1answer
73 views

### Motivation for the Deformed Nekrasov Partition Function

I have recently been doing research on the AGT Correspondence between the Nekrasov Instanton Partition Function and Louiville Conformal Blocks (http://arxiv.org/abs/0906.3219). When looking at the ...
1answer
51 views

### Error in variance

I've been exploring techniques in statistical physics, specifically applying them to spin ices. I'm in the canonical ensemble. By using the fluctuation dissipation theorem you can extract useful ...
1answer
96 views

### Energy density of a quantum mechanical ensemble

How do we determine the energy density of a given system? I have seen that the density operator $$\rho~=~\frac{\exp(-\beta \hat{H})}{\text{tr}(\exp(-\beta \hat{H}))}.$$ What does this mean exactly ...
1answer
62 views

### Basic energy calculation for N identical spin system

We have a system that has N identical spins $n_i$, and each spin can be in state 1 or 0. The overall energy for the system is $\epsilon\sum_{i=1}^{N}n_i$. My understanding: There is only one ...
1answer
45 views

### Bose-Einstein condensate for general interacting systems

There is Bose-Einstein condensate (BEC) for non-interacting boson systems. Can we prove the existence of BEC for interacting systems?
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28 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 ...
1answer
33 views

### How can I find the temperature of this system?

A system was given a small amount of thermal energy dE, and its number of states G grew by 25%. How can I find the system temperature? The system contains gas particles, I know that \$dE << ...
1answer
75 views

### Mean-field theory and spatial correlations in statistical physics

In statistical physics, mean-field theory (MFT) is often introduced by working out the Ising model and it's properties. From a spin model point of view, the mean-field approximation is given by ...
1answer
54 views

### Deriving the change in the Helmholtz free energy in the context of the free energy perturbation method

I am reading Free Energy Calculations: Theory and Applications in Chemistry and Biology by Chipot and Pohorille. At the beginning of the text (page 19, for example), the authors define the Helmholtz ...
0answers
6 views

### Hardware random number generator Vs. Pseudo random number generator in the battlefield of Markov Chain Monte Carlo processes [migrated]

I'm implementing a Markov Chain Monte Carlo process for a Quantum Monte Carlo routine, in every book and paper I've read so far the success of the routine and quality of the results strongly depends ...
2answers
48 views

### Has anyone studied a statistical scaling law for the universe? [closed]

How do named objects in the universe scale? Is there a predictable curve for an ordered list, say {atom, animal, planet, solar system, galaxy, etc}? Can you then use the analysis to predict when the ...
0answers
92 views

### What is the condition for getting Bose-Einstein condensation? [closed]

Consider an ideal Bose gas in three dimension with energy-momentum relation E proportional to $p^s$ with $s>0$. Find the range of $s$ for which this system may undergo a Bose-Einstein ...
0answers
63 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) ...
1answer
83 views

### Accessible microstates of harmonic oscillator in microcanonical enemble

While reading up on statistical physics, I am going through the calculation of the partition function of the harmonic oscillator in the microcanonical ensemble. The result for the partition function ...
1answer
72 views

### Uncertainty and Thermodynamics

Dilemma The uncertainty principle of energy and the 2nd law of thermodynamics don't add up : the uncertainty principle of energy says that \$\Delta \tau \cdot \Delta E \ge \frac{h}{4\pi} = ...
1answer
62 views

### Maximizing Multiplicity of Einstein Solid == (Temperature = $\infty$)?

If I have a system consisting of 2 Einstein solids (A and B) is it equivalent to say that maximizing the multiplicity of the ...
0answers
26 views

### Increase in number of micro states explanation or restatement of second law?

Is the boltzmann's expression of entropy as log of micro states leading to the formulation that system is more likely to be in a macrostate with more no. Of micro states really is an explanation or ...
0answers
71 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 ...
2answers
132 views

### Energy of particle in electric field

I'm taking a physics class and the professor teaches us really basic things in lecture and then gives homework way beyond what he taught in lecture. Obviously I need to find some resource other than ...
1answer
115 views

### Why the chemical potential of massless boson is zero? [duplicate]

In Bose-Einstein condensation, the chemical potential is less than the ground state energy of the system($\mu<\epsilon_g$). But why does the massless boson such as photon have zero chemichal ...
0answers
150 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 $B\to 0$ $$\chi = \frac{dM}{dB} \approx \frac{n\,\mu^{*^2}}{k\,T}\,\frac{f_{1/2}(z)}{f_{3/2}(z)}$$ ...
2answers
183 views

### Does entropy really always increase (or stay the same)?

Consider this image. If the big (grey) molecules were all to spontaneously move to the left, and the small ones were to move to the right, there would be an increase in order. While unlikely, ...
1answer
65 views

### classical quantum particles in grand canonical ensemble

To derive Bose-Einstein and Fermi-Dirac distribution, we need to apply grand canonical ...
1answer
57 views

### Differences between hard-core boson and fermion

Hard boson has strong repulsion with each other just like fermion. What is the differences between hard-cord boson and fermion. Which materials are hard-core bosons?
1answer
72 views

### Change of variables, Fermi Integral

This is a really basic question, but I'm kind of confused. I have this integral $$\int_{0}^{\infty}\frac{p^{2}dp}{e^{\alpha+\beta p^{2}/2m}+1}$$ where ...
2answers
89 views

### What is wrong with these ways of determining the mean occupation number?

Could anyone point out what went wrong in this argument? Setup: We have a system with 2 energy levels say with energies $0,e$ respectively. We consider the grand canonical ensemble for the system ...
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 ...
1answer
77 views

### Local minima in Ising model in a Monte Carlo simulation

Is there any way to check whether in a Monte Carlo simulation using Ising model is stuck in any (false) local minima of energy or not, particularly in 3D system ?
1answer
217 views

### Bohr-van Leeuwen theorem and quantum mechanics

Preamble: If one considers an ideal gas of non interacting charged particles of charge $q$ in a uniform magnetic field $\mathbf{B} = \mathbf{\nabla} \wedge \mathbf{A}$, then the classical partition ...
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