## 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 T_{co}, 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 language | English |
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Article number | 020 |

Pages (from-to) | 2247-2256 |

Number of pages | 10 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 17 |

Issue number | 11 |

DOIs | |

State | Published - 1 Dec 1984 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy