Crossover scaling functions for exchange anisotropy:X Yand planar models

The crossover behavior of the susceptibility ${\chi }^{xx}$ of classical $X Y$ and planar models with anisotropic exchange coupling is studied on the basis of the extended scaling hypothesis. The universality of the scaling function with respect to lattice type (fcc and sc) and model type ($X Y$ and planar $n=2\mathrm{}$ models) is confirmed. The scaling function for ${\chi }^{xx}\mathrm{}(T,g)\mathrm{}$ is obtained by analyzing the high-temperature-series coefficients expressed as polynomials in $g$, the anisotropy parameter. The crossover of $\gamma$, the susceptibility exponent, is plotted, using the calculated scaling function, over a wide range of temperatures.