TY - JOUR

T1 - Random field Ising model on the Bethe lattice

AU - Wohlman, O. E.

AU - Domb, C.

PY - 1984

Y1 - 1984

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=36149038530&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/17/11/020

DO - 10.1088/0305-4470/17/11/020

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AN - SCOPUS:36149038530

SN - 0305-4470

VL - 17

SP - 2247

EP - 2256

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 11

M1 - 020

ER -