Scaling approach to spin-glass phenomena

The scaling model of spin-glass phenomena is extended to consider both longitudinal and transverse order parameters $q_1$ and $q_t$. The lowest-order coupling in the free energy goes as $q_l^2{q}_t^2$. The field ($h$) dependence of the reduced temperature $t$ for transverse freezing is found to be $t\sim h^{\frac{4}{\delta }}$ where $\delta$ is the conventional nonlinear susceptibility field exponent ($\chi \sim h^{\frac{2}{\delta }}$). While the transverse correlation length diverges at $t=0\mathrm{}$, the longitudinal correlation length remains finite.