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The study of physical systems using probabilistic reasoning, especially relating small-scale classical mechanics to large-scale thermodynamics.

18 votes
3 answers
1k views

Ising model on groups

Can anything interesting be deduced about the properties of a group from the behavior of the Ising model on its Cayley graph? (i.e. existence and character of phase transitions, critical behavior) I'm …
Marcin Kotowski's user avatar
14 votes
1 answer
549 views

Ising model - phase transition vs rapid mixing

Consider a graph $G=(V,E)$ and Ising model on that graph, i.e. configuration space is $\Omega=${$-1,+1$}$^V$ and energy of a configuration $s \in \Omega$ is given by: $H(s) = -\beta \sum_{u \sim v}s(u …
Marcin Kotowski's user avatar