Phase Transition in a Dzyaloshinsky-Moriya Spin-Glass

Abstract

A mean-field model of a Heisenberg spin-glass with weak random anisotropy is solved. It is shown that an Ising-like phase transition in a finite magnetic field $H$ occurs at $T_c\mathrm{}\left(H\right)\mathrm{}\sim T_c\mathrm{}\left(0\right)-A{H}^{\frac{2}{3}}$ in the limit of small $H$. The crossover to an Ising behavior occurs when $\frac{D}{J}>{\left(\frac{\mu H}{J}\right)}^{\frac{2}{3}}$, where $D$ and $J$ are the anisotropy and exchange coupling constants, respectively.