Weakly diluted n >= 2 Ising antiferromagnets: Loss of long-range order and crossover effects.

Abstract

The effect of small amounts of bond or site dilution on n\ensuremath{\ge}2 Ising antiferromagnets (AF) in zero external field is studied. It is shown (a) that such impurities generate spatially random symmetry breaking, much like a random anisotropy along a few axes; (b) that any small amount of these impurities obliterates long-range order in d<2 (and very likely in d=2) dimensions in these systems; and (c) that the corresponding crossover exponent for these systems is, for any spatial dimensionality, \ensuremath{\varphi}=\ensuremath{\gamma}-2\ensuremath{\beta} (instead of \ensuremath{\varphi}=\ensuremath{\alpha}, as prescribed by the Harris criterion for random ferromagnets). Both transfer-matrix (TM) and Monte Carlo (MC) results are obtained for an Ising AF with nearest- and next-nearest-neighbor interactions. The TM data, obtained for long narrow strips at low temperature, and the MC results, for two-dimensional systems in the critical region, support the above conclusions.