# 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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### Estimating Partition functions

I have a finite state ensemble with an energy functional (you can think of it as an ferromagnetic Ising model if you like), and I need very careful estimates of the partition function. What methods ...
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### Entropy of a polymer contained in a sphere with infinitely thin chords

Imagine that I have a polymer (approximated as a freely diffusing, freely jointed chain with some number of subunits 'N'), and I place this polymer into a sphere of some volume 'V'. Next, I proceed to ...
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### Where can I find a good classification for phase transitions?

I'm having a hard time to find a good (and modern) classification scheme for phase transitions and related universality classes. Can someone recommend a paper/book/site? Detailed mathematical aspects ...
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### Accuracy of the Boltzmann equation

I have had this question for some time now. Hopefully someone can answer it. I know that the Boltzmann equation is widely regarded as a cornerstone of statistical mechanics and many applications have ...
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### Why is Avogadro's hypothesis true?

Why is the number of molecules in a standard volume of gas at a standard temperature and pressure a constant, regardless of the molecule's composition or weight? Let's say I have a closed box full of ...
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### What is known about some massive Gaussian models on a lattice?

Recently I started to play with some massive Gaussian models on a lattice. Motivation being that I work on massless models and want to understand the massive case because it seems easier to handle (e....
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### What is the difference between thermodynamics and statistical mechanics?

What is the difference between thermodynamics and statistical mechanics?
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### Is temperature in vacuum zero?

From Wikipedia entry on Kinetic Theory The temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms. Now if I remove all the particles from the box shown ...
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### Which areas in physics overlap with those of social network theory for the analysis of the graphs?

I am studying social networks in terms of graph theory and linear algebra. I know that physicists have published and worked a lot in this field. This causes me to assume that there are sub-fields in ...
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### Irreversible expansion and time reversal symmetry

Suppose there are N non-interacting classical particles in a box, so their state can be described by the $\{\mathbf{x}_i(t), \mathbf{p}_i(t) \}$. If the particles are initially at the left of the box, ...
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### Ising model for dummies

I am looking for some literature on the Ising model, but I'm having a hard time doing so. All the documentation I seem to find is way over my knowledge. Can you direct me to some documentation on it ...
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### How many Onsager's solutions are there?

Update: I provided an answer of my own (reflecting the things I discovered since I asked the question). But there is still lot to be added. I'd love to hear about other people's opinions on the ...
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### What happens for the spins around the phase transition

Suppose we now consider a lattice of spin, say Ising model, and the phase transition at the critical temperature $T_c$. There are few scaling laws describe the regime around the critical temperature ...
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### Home experiment to estimate Avogadro's number?

How to get an approximation of Avogadro or Boltzmann constant through experimental means accessible by an hobbyist ?
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### Is there a four-dimensional definition of entropy?

It seems odd that entropy is usually only defined for a system in a single 'slice' of time or spacelike region. Can one define the entropy of a system defined by a 4d region of spacetime, in such a ...
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### Maxwell's Demon Constant (Information-Energy equivalence)

New Scientist article: Summon a 'demon' to turn information into energy The speed of light c converts between space and time and also appears in $E=mc^2$. Maxwell's Demon can turn information ...
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### Are the physical laws scale-dependent?

If you read the article "More Is Different", by P.W. Anderson (Science, 4 August 1972), you will find a deep question: are the physical laws dependent of the size of the system under study? As an ...
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### Two-point correlation function for planar Potts model

Fastest known method for computing Potts model partition function (Bedini and Jacobsen's "A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, ...