Critical behaviour of the random-anisotropy model in the strong-anisotropy limit

Abstract

We investigate the nature of the critical behaviour of the random-anisotropy Heisenbergmodel (RAM), which describes magnetic systems with random uniaxial single-siteanisotropy, such as some amorphous alloys of rare earths and transition metals. Inparticular, we consider the strong-anisotropy limit (SRAM), in which the Hamiltonian canbe rewritten as the one of an Ising spin-glass model with correlated bond disorder. Weperform Monte Carlo simulations of the SRAM on simple cubic lattices of linear sizeL, upto L = 30, measuring correlation functions of the replica–replica overlap, which is the order parameter ata glass transition. The corresponding results show critical behaviour and finite-size scaling.They provide evidence of a finite-temperature continuous transition with critical exponentsηo = −0.24(4) and νo = 2.4(6). These results are close to the corresponding estimates that have been obtained in the usualIsing spin-glass model with uncorrelated bond disorder, suggesting that the two models belong tothe same universality class. We also determine the leading correction-to-scaling exponent, findingω = 1.0(4).