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Nov
19
revised What are alternative ways to think about transfer matrix as used in Ising model?
Added a (hopefully helpful) remark...
Nov
18
revised What are alternative ways to think about transfer matrix as used in Ising model?
Corrected typos
Nov
14
revised What are alternative ways to think about transfer matrix as used in Ising model?
Further typos...
Nov
14
revised What are alternative ways to think about transfer matrix as used in Ising model?
Typo corrected
Nov
14
revised What are alternative ways to think about transfer matrix as used in Ising model?
Added context
Nov
14
answered What are alternative ways to think about transfer matrix as used in Ising model?
Oct
26
comment Why is the second law of thermodynamics indisputable?
Sure. But the 2nd law only applies to large systems and for those it should be generically true. Nobody is saying that it is the answer to all fundamental aspects of Physics ;) . Only that, because it is a generic property of large systems, it will remain true essentially unchanged, while paradigms about the fundamental nature of things will still change many, many times.
Oct
26
comment Why is the second law of thermodynamics indisputable?
I think that we agree on the status of fundamental theories. However, the "regions of validity" statement most probably does not apply to the second law of thermodynamics as it does to other physical theories. Indeed, the 2nd Law is probably going to remain valid, although its precise statement might evolve with time (as it had to become more precise after Boltzmann realized its statistical nature). In a sense, it is more of a "meta-law": its validity is the consequence of features which are mostly insensitive to the details of the underlying theory.
Oct
26
comment Why is the second law of thermodynamics indisputable?
I agree with @EmilioPisanty. I expect that, as time goes by, what we consider the "fundamental" description of Nature will still change many times, as its scope encompasses larger and larger domains. However, most people have no doubt that (a proper version of) the second law of thermodynamics will continue to hold, irrespective of what our current pet fundamental theory is.
Oct
25
awarded  statistical-mechanics
Oct
24
comment Thermodynamics for 1D line of 3D dipoles
I don't know whether explicit expressions can be obtained, but I doubt it. Nevertheless, as long as the interaction decays faster than $1/(i-j)^2$, there will be no phase transition. Indeed, there is a very general theorem that tells you the following: if the maximal interaction energy between an interval of length $n$ and the rest of the line is bounded uniformly in $n$ (which is the case if the interaction decays fast enough), then there is a unique infinite-volume Gibbs measure.
Oct
7
comment Ising model at high vs. low temperature
It is not clear at all to me what the question really is. A lot is know about properties of these Gibbs measures, so it will probably be possible to answer your question once you have clarified it. (Note, in particular, that the spins form an iid Bernoulli field only at infinite temperature, and that the measure you get at any two distinct temperatures are mutually singular, so you should make the notion of distance you want more precise).
Oct
4
awarded  Nice Answer
Aug
31
comment Is the MaxEnt “interpretation” of statistical mechanics the current mainstream approach?
Sure, but a interpretation of probabilities in statistical mechanics is the core of any derivation of the latter. MaxEnt provides a subjective interpretation of the latter, the ergodicity/mixing approaches attempt (and fail) to provide a mechanical interpretation. I don't see how large deviations theory can be considered as an "alternative" approach to MaxEnt in this respect, as it has exactly nothing at all to say about this issue.
Aug
30
comment Is the MaxEnt “interpretation” of statistical mechanics the current mainstream approach?
I don't see what you mean by "getting the statistical physics framework based on the theory of large deviations". Large deviations theory, by definition, requires a probabilistic framework, which is precisely what is difficult to derive in an objective way from the underlying mechanical theory. The only thing that large deviations help you with is moving from one description (say, microcanonical) to another one (say, canonical). But you'd still need to derive the microcanonical probability measure in some way, and this is the hard part.
Aug
28
revised Reference for mathematics of statistical mechanics
Added a link
Aug
28
revised Reference for mathematics of statistical mechanics
Added a couple of additional references...
Aug
27
answered Reference for mathematics of statistical mechanics
Aug
13
comment Critical temperature and lattice size with the Wolff algorithm for 2d Ising model
@ACuriousMind: Done (but it is a bit sketchy, as I don't have so much time now; in particular, it would be nice to provide a picture of the specific heat for the 2d Ising model on a finite torus, as well as the limit quantity).
Aug
13
answered Critical temperature and lattice size with the Wolff algorithm for 2d Ising model