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. $Dlog$ Pad\'e analyses give a susceptibility exponent $\ensuremath{\gamma}$ in $d=3$ which crosses over from 1.24 in the pure limit to 1.40 as disorder increases.