Cutoff corrections to Gaussian-Heisenberg crossover behaviour

Abstract

The crossover behaviour between Gaussian and Heisenberg critical behaviour is studied in an isotropic n-vector model, in which the effect of a lattice cutoff, a= Lambda ^-1, is imitated by means of (nabla² phi )² and (nabla nabla² phi )² terms in the effective Hamiltonian. A field theoretic method is used to construct, to first order in in =4-d, a crossover scaling function for the susceptibility containing the corrections to scaling which involve Lambda directly. The leading corrections vanish, near the Heisenberg fixed point, as ((T-T_c)^v/ Lambda )² where v is the corresponding correlation length exponent, and near the Gaussian fixed point as ((T-T_c)¹2// Lambda )².