Ising Model in a Quenched Random Field: Critical Exponents in Three Dimensions from High-Temperature Series

Abstract

A formalism is given whereby high-temperature series for the random-field Ising model on a $d$-dimensional hypercubic lattice is obtained by a partitioning of the vertices of the pure-Ising-series diagrams. For a bimodal distribution of quenched random fields we determine the series for the susceptibility to seventh order. Order by order the disorder is treated exactly. $Dlog$ Padé analyses give a susceptibility exponent $\gamma$ in $d=3\mathrm{}$ which crosses over from 1.24 in the pure limit to 1.40 as disorder increases.