Equilibrium spin-glass transition of magnetic dipoles with random anisotropy axes

Abstract

We study fully occupied lattice systems of classical magnetic dipoles which point along random axes. Only dipolar interactions are considered. From tempered Monte Carlo simulations, we obtain numerical evidence that supports the following conclusions: in three dimensions, (a) there is an equilibrium spin glass phase at temperatures below $T_c$, where $k_BT_c= (0.86\pm 0.07)\varepsilon_d $ and $\varepsilon_d$ is a nearest neighbor dipole-dipole interaction energy, (b) in the spin glass phase the overlap parameter is approximately given by $\sqrt{1-T/T_c}$, and (c) the correlation length $\xi$ diverges at $T_c$ with a critical exponent $\nu =1.5\pm0.5$; in two dimensions $\xi$ diverges at or near T=0 and $\nu=3\pm1$.