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Journal of Applied Physics

Spin-glass transition in the random anisotropy axis model

Amitabha Chakrabarti

Published Apr 15, 1988• 7 citations
Publisher

Abstract

The critical behavior of the Random Anisotropy Axis model (RAM) is studied by the Monte Carlo simulation method in the limit of infinite anisotropy. Finite size scaling analysis of the data for equilibrium averages strongly suggests a zero temperature critical point in two dimensions and a finite temperature phase transition in three dimensions. The values of the critical exponents in both two and three dimensions indicate that RAM belongs to the same universality class as that of short-range Ising spin-glass models.

DOI
10.1063/1.341163

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The critical behavior of the Random Anisotropy Axis model (RAM) is studied by the Monte Carlo simulation method in the limit of infinite anisotropy. Finite size scaling analysis of the data for equilibrium averages strongly suggests a zero temperature critical point in two dimensions and a finite temperature phase transition in three dimensions. The values of the critical exponents in both two and three dimensions indicate that RAM belongs to the same universality class as that of short-range Ising spin-glass models.
The random anisotropy axis model (RAM) in two dimensions (d=2) is studied in the limit of infinite anisotropy strength using the large-cell renormalisation group method. It is found that the model exhibits a 'zero-temperature phase transition', to a nonferromagnetic ground state, with critical exponents consistent with those of the d=2 Ising spin glass model. It is concluded that the RAM belongs to the universality class of the Ising spin glass, at least for d=2 and probably for all d<or=4.
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).
We study a short-range site-random Ising model in three dimensions (3D) using a Monte Carlo (MC) method and find a phase transition to a spin glass (SG) phase at a very high temperature ( T c ≃2.83 J). Values of the critical exponents estimated from a finite-size scaling analysis are different from those in both the 3D∓J\mp J∓J Ising model and the 3D Ising ferromagnet. We suggest that the SG phase in this model is a new SG phase which is characterized by a nonzero SG order parameter q ≠0.
We present results of a Monte Carlo simulation study of the zero-temperature quantum phase transition of a three-dimensional short-range spin-1/2 Ising spin glass, driven by a transverse magnetic field. This quantum transition is equivalent to the finite-temperature transition in the (3+1)-dimensional anisotropic classical random Ising model that is the path integral of the quantum system. The critical exponents are estimated using a finite-size scaling analysis. The uniform linear susceptibility is finite at the transition, while the nonlinear susceptibility diverges. The results are more consistent with conventional, rather than activated, dynamic scaling in the quantum system.