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

Details Critical behavior of the random-anisotropy model in the strong-anisotropy limit Critical behavior of the random-anisotropy model in the strong-anisotropy limit

2006-04-05

arxiv.org/abs/cond-mat/0604124v2

J. Stat. Mech. (2006) P06002

Physics

Condensed Matter

Disordered Systems and Neural Networks

24 pages, 13 figs, J. Stat. Mech. in press

Scientific paper

10.1088/1742-5468/2006/06/P06002

We investigate the nature of the critical behavior 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. We perform 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 behavior 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. We also determine the leading correction-to-scaling exponent finding $\omega = 1.0(4)$.

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