Equations of state for bicritical points. I. Calculations in the disordered phase

Equations of state are calculated for anisotropic spin Hamiltonians suitable for describing the spin-flop transition in materials such as GdAl${\mathrm{O}}_3$ and Mn${\mathrm{F}}_2$. Crossover scaling functions for the specific heat, nonordering susceptibility, and parallel and transverse susceptibilities are derived to first order in $\epsilon =4-d$ directly from renormalization-group recursion relations.