Crossover scaling function for the free energy

A cubic field, coupling tos|s|², inn-component spin models induces a bicritical crossover fromn-isotropic to Ising like (m=1) critical behaviour for 1<n<, but to classical behaviour in the limitn. By following the analysis of Nelson and Domany, the bicritical scaling function for the free energy ind dimensions is obtained correct to order =4–d and for general (m,n). The mechanism responsible for the breakdown of hyperscaling in the classical behaviour is discussed.