Random field Ising model on the Bethe lattice

O. E. Wohlman, C. Domb

Research output: Contribution to journalArticlepeer-review

Abstract

Low-temperature series expansions have been derived for the random field Ising model with a delta -function distribution on a Bethe lattice by two independent methods: (a) the finite-cluster method which uses graph embeddings and appropriate weighting functions; (b) the use of a recursion relation specific to the Bethe lattice. Numerical values have been evaluated when the coordination number q=3, 4 and the coefficients analysed to assess critical behaviour. For small fields, and temperatures near to Tco, the critical exponent of the magnetisation seems to retain its mean-field value. But there is clear evidence of a change in critical behaviour at some point on the critical curve. It is argued that when q>3 a tricritical point is indicated as found by Aharony in his mean-field solution.

Original languageEnglish
Article number020
Pages (from-to)2247-2256
Number of pages10
JournalJournal of Physics A: Mathematical and General
Volume17
Issue number11
DOIs
StatePublished - 1984
Externally publishedYes

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