2006/06/28 by Francesco Parisen Toldin, Andrea Pelissetto, Toldin, Francesco Parisen +3
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/0606728
6 pages, 4 figures. Submitted to JPCM. Proceedings of HFM2006, August 15-19, Osaka, Japan
arxiv created 2006/06/28 · openalex publication_date 2006/06/28 · 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 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 ∑< xy > jxy σx σy, where jxy = ux ⋅ uy and ux is a random three-component unit vector. We performed Monte Carlo simulations of the SRAM on simple cubic L3 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 ηo=-0.24(4) and νo=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.