The random-anisotropy model in the strong-anisotropy limit

TL;DR

This study investigates the critical behavior of the strong-anisotropy limit of the random-anisotropy Heisenberg model, revealing a finite-temperature transition with critical exponents similar to the Ising spin-glass universality class.

Contribution

The paper demonstrates that the strong-anisotropy limit of the RAM exhibits a continuous glass transition with critical exponents akin to the uncorrelated Ising spin-glass model, suggesting universality class equivalence.

Findings

Evidence of a finite-temperature continuous transition.

Critical exponents ta_o=-0.24(4) and mbda_o=2.4(6).

Disorder correlations are irrelevant for universality.

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} \sigma_x \sigma_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 \eta_o=-0.24(4) and \nu_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.