Universal amplitudes in anisotropic Heisenberg systems

Abstract

Feynman graph methods are used to analyse crossover behaviour in an n-component Heisenberg system, with a spin anisotropy that results asymptotically in m-component critical behaviour. An expression for the universal n- and m-dependent amplitude locating the singularity of the crossover scaling function is derived to second order in epsilon =4-d and found to give fair agreement with the results of recently derived series expansions. The same techniques are used to obtain, to 0( epsilon ²), a universal amplitude ratio characterizing the shape of the phase boundary in the vicinity of spin-flop bicritical point.