00-418 Bleher P., Ruiz J., Schonmann R.H., Shlosman S., Zagrebnov V.
Rigidity of the critical phases on a Cayley tree. (182K, LATeX) Oct 24, 00
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Abstract. We discuss statistical mechanics on non-amenable graphs, and we study the features of the phase transition, which are due to non-amenability. For the Ising model on the usual lattice it is known that fluctuations of magnetization are much less likely in the states with non-zero magnetic field than in the pure states with zero field. We show that on the Cayley tree the corresponding fluctuations have the same order.

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