Rigidity of the Critical Phases on a Cayley Tree

  title={Rigidity of the Critical Phases on a Cayley Tree},
  author={Jean Charles Ruiz and Roberto H. Schonmann and Senya B. Shlosman and Valentin A. Zagrebnov},
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 below the critical temperature 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. 2000 Math. Subj. Class. 60F10, 82B20. 

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