Amenability and Phase Transition in the Ising Model
نویسنده
چکیده
We consider the Ising model with external eld h and coupling constant J on an innnite connected graph G with uniformly bounded degree. We prove that if G is nonamenable, then the Ising model exhibits phase transition for some h 6 = 0 and some J < 1. On the other hand, if G is amenable and quasi{transitive, then phase transition cannot occur for h 6 = 0. In particular, a group is nonamenable if and only if the Ising model on one (all) of its Cayley graphs exhibits a phase transition for some h 6 = 0 and some J < 1.
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تاریخ انتشار 1998