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4

wsc's answer (i.e., Onsager's computation of the free energy) provides one alternative road to a proof of a phase transition in the Ising model. It implies the existence of a phase transition in dimension 2 (for the nearest-neighbor model). Combined with correlation inequalities, this implies existence of a phase transition in any dimension d≥2, and ...

1

The $d=2$ (square lattice) Ising model has a special "duality" property (the high-temperature and low-temperature partition functions can be mapped on to one another) discovered by Kramers & Wannier in 1941. This doesn't rigorously prove that a phase transition exists, but it remarkably predicts the critical point where a phase transition, if it did ...

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Perhaps this isn't quite the answer you're seeking, but you may be interested in the phenomena of thermoremanent and isothermal remanent magnetization. Basically, if you perform a deep quench on a spin glass (i.e., freeze the spins) in a uniform external magnetic field and then, after some time, switch off the magnetic field, (or alternatively, quench ...

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