This article is cited in 59 papers

Partition structures of the Cayley tree and applications for describing periodic Gibbs distributions

U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: The disposition order of partition elements into adjacent classes of the group representation of the Cayley tree on its finite index normal subgroups is described. For the inhomogeneous Ising model it is proved that there exist three $H_0$-periodic Gibbs distributions, where $H_0$ is a normal subgroup of finite index.

Received: 05.08.1996
Revised: 16.01.1997

DOI: 10.4213/tmf1037

 English version: Theoretical and Mathematical Physics, 1997, 112:1, 929–933

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