 00418 Bleher P., Ruiz J., Schonmann R.H., Shlosman S., Zagrebnov V.
 Rigidity of the critical phases on a Cayley tree.
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Oct 24, 00

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Abstract. We discuss statistical mechanics on nonamenable graphs, and we study
the features of the phase transition, which are due to nonamenability.
For the Ising model on the usual lattice it is known that fluctuations
of magnetization are much less likely in the states with nonzero
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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