Equations of state for bicritical points. III. Cubic anisotropy and tetracriticality

Abstract

Crossover scaling functions for a two-component spin system with quadratic anisotropy $g$ and cubic anisotropy $\tilde{v}$ are calculated to first order in $\epsilon =4-d$ and in $\tilde{v}$, near the transitions within the ordered phases below the multicritical point ($T=T_m,g=0\mathrm{}$). Emphasis is placed on the mechanism by which the system is driven to bicritical or tetracritical behavior by the dangerous irrelevant variable $\tilde{v}$. Explicit expressions and graphs for the various thermodynamic scaling functions are presented.