Crossover behaviour and effective critical exponents in isotropic and anisotropic Heisenberg systems

Abstract

Renormalisation group methods are used to determine, to second order in epsilon =4-d, the scaling function describing the crossover from Gaussian to Heisenberg behaviour in the susceptibility of an isotropic n-component spin system. The results are used in conjunction with an earlier Feynman graph calculation to obtain an O( epsilon ²) representation of the n-to-m-component susceptibility crossover function, and the corresponding effective exponents, for an anisotropic n-component system.