2006/04/30 by Francesco Parisen Toldin, Andrea Pelissetto, Ettore Vicari · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1088/1742-5468/2006/06/p06002
published as J. Stat. Mech. (2006) P06002 · 24 pages, 13 figs, J. Stat. Mech. in press
arxiv created 2006/05/04 · openalex publication_date 2006/06/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
We investigate the nature of the critical behaviour of the random-anisotropy Heisenberg model (RAM), which describes magnetic systems 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 lattices of linear size L , 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. We also determine the leading correction-to-scaling exponent, finding ω = 1.0(4).