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

Abstract

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 $\omega =1.0(4)$.

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

References in corpus (3)

• The critical exponents of the superfluid transition in He4
• Feedback-optimized parallel tempering Monte Carlo
• Critical behavior of the three-dimensional bond-diluted Ising spin glass: Finite-size scaling functions and Universality

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