Bleher P., Ruiz J., Schonmann R.H., Shlosman S., Zagrebnov V.
Rigidity of the critical phases on a Cayley tree.
(182K, LATeX)
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.