Dynamics of vector spin glasses with random anisotropy

Abstract

The dynamics of vector spin glasses with additional random anisotropy is investigated in the mean field approximation. We find a cross-over of the upper critical line from a behaviour of Heisenberg spins with a field-temperature dependence$\tilde T_f - T \propto H^2$, for large fieldsH, to Ising like behaviourT _f −T∝T ^2/3, for small fields and fixed anisotropy, in agreement with results of Kotliar and Sompolinsky. Here,$\tilde T_f$ andT _f are characteristic spin glass temperatures. In addition, one has a second line with reversed behaviour which presumably represents a cross-over line from weak to strong non-ergodicity. The local transverse susceptibility χ _T (ω) varies for large fields and ω→0 along the upper critical line as ω^vT, with a critical exponentV _T = 1/2 − 11D/60 πJ, whereD andJ are the anisotropy and exchange coupling constants, respectively. On the Ising-like part of the upper critical line one has isotropic spin glass parameters,q _L =q _T , and susceptibilities, and a critical exponent,$v = 1/2 - {{\sqrt 3 ({{5h^2 } \mathord{\left/ {\vphantom {{5h^2 } 4}} \right. \kern-\nulldelimiterspace} 4})^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} } \mathord{\left/ {\vphantom {{\sqrt 3 ({{5h^2 } \mathord{\left/ {\vphantom {{5h^2 } 4}} \right. \kern-\nulldelimiterspace} 4})^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} } \pi }} \right. \kern-\nulldelimiterspace} \pi }$ which is similar to that of Ising spins along the de Almeida-Thouless line.