The random-anisotropy model in the strong-anisotropy limit

Abstract

We investigate the nature of the critical behaviour of the random-anisotropy Heisenberg model (RAM), which describes a magnetic system with random uniaxial single-site anisotropy, such as some amorphous alloys of rare earths and transition metals. In particular, we consider the strong-anisotropy limit (SRAM), in which the Hamiltonian can be rewritten as the one of an Ising spin-glass model with correlated bond disorder: H = - J \sum_{< xy >} j_{xy} σ_x σ_y, where j_{xy} = \vec{u}_x \cdot \vec{u}_y and \vec{u}_x is a random three-component unit vector. We performed Monte Carlo simulations of the SRAM on simple cubic L^3 lattices, up to L=30, measuring correlation functions of the replica-replica overlap, which is the order parameter at a glass transition. The corresponding results show critical behaviour and finite-size scaling. They provide evidence of a finite-temperature continuous transition with critical exponents η_o=-0.24(4) and ν_o=2.4(6). These results are close to the corresponding estimates that have been obtained in the usual Ising spin-glass model with uncorrelated bond disorder, suggesting that the two models belong to the same universality class. This is consistent with arguments that suggest that the disorder correlations present in the SRAM are irrelevant.