Quadratic spatial anisotropy model with singularities: comparison between exact solution and renormalisation group for crossover dependence

Abstract

The authors consider a quadratic spatially anisotropic model, with a (d-dperpendicular to )-dimensional defect hyperplane embedded in d space, and provide the exact solution for the defect hyperplane correlation length and susceptibility for arbitrary epsilon perpendicular to =2-dperpendicular to >0. A perturbation expansion in the defect surface interaction displays singularities in epsilon perpendicular to and therefore requires renormalisation. Renormalisation group descriptions of the crossover dependence of scaling amplitudes on the strength of the surface interaction are compared with the exact analytic solution. The close analytic similarities between the renormalisation group crossovers for scaling amplitudes in the spatially anisotropic model and in phi 4 field theory suggests that the results for the former have a bearing on the expected faithfulness of the latter.