Scaling approach to spin-glass phenomena

Abstract

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 $t\ensuremath{\sim}{h}^{\frac{4}{\ensuremath{\delta}}}$ where $\ensuremath{\delta}$ is the conventional nonlinear susceptibility field exponent ($\ensuremath{\chi}\ensuremath{\sim}{h}^{\frac{2}{\ensuremath{\delta}}}$). While the transverse correlation length diverges at $t=0$, the longitudinal correlation length remains finite.