Cubic fields, bicritical crossover, the spherical and van der Waals limits

A cubic field coupling to s mod s mod 2 , in n-component spin models induces a bicritical crossover from n-isotropic to Ising-like (m=1) critical behaviour for 1<n< infinity , but to classical behaviour in the limit n to infinity . The mechanism for this is explained and related to the van der Waals or infinite-range crossover. By following the analysis of Nelson and Domany (1976), the bicritical scaling function for the parallel susceptibility in d dimensions is obtained correct to order epsilon =4-d and for general (m,n) in a form correctly reproducing all limits; the effective exponent, gamma eff , is examined numerically in various regimes.