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Journal of Magnetism and Magnetic Materials

Critical behavior of spin systems with quenched disorder

Akai Kurbanovich Murtazaev, Ibragimkhan K. Kamilov, Albert Babaevich Babaev

Published Nov 19, 2005• 4 citations
Publisher
DOI
10.1016/j.jmmm.2005.10.210

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A Monte Carlo method is applied to simulate the static critical behavior of a cubic-lattice 3D Ising model for systems with quenched disorder. Numerical results are presented for the spin concentrations of p = 1.0, 0.95, 0.9, 0.8, 0.6 on L × L × L lattices with L = 20–60 under periodic boundary conditions. The critical temperature is determined by the Binder cumulant method. A finite-size scaling technique is used to calculate the static critical exponents α, β, γ, and ν (for specific heat, susceptibility, magnetization, and correlation length, respectively) in the range of p under study. Universality classes of critical behavior are discussed for three-dimensional diluted systems.

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This work provides a full description of the critical behavior of the XX spin-1/2 chain under correlated quenched disorder.Previous investigations have shown that the introduction of correlation between couplings in the random XX model gives rise to a novel critical behavior, where the infinite-randomness critical point of the uncorrelated case is replaced by a family of finite-disorder critical points that depends on the disorder strength.Here it is shown that most of the critical exponents of the XX model with correlated randomness are equal to clean (without disorder) chain values and do not depend on disorder strength, except the critical dynamical exponent and the anomalous dimension.The former increases monotonically with disorder strength, whereas the results obtained for the latter are unreliable.Furthermore, the scaling relations between the critical exponents were also tested and it was found that those involving the system dimensionality, namely the hyperscaling and Fisher's scaling relations, are not respected.Measurements of the Rényi entanglement entropy of the system at criticality have also been performed, and it is shown that the scaling behavior of the correlated-disorder case is similar to the theoretical prediction for the clean chain, displaying the same finite-size correction and a disorder-dependent effective central charge in the leading term of the scaling.Further corrections to the scaling of the entanglement entropy were also investigated, but the results are inconclusive.The model was studied via exact numerical diagonalization of the corresponding Hamiltonian.
A Monte Carlo method is applied to simulate the static critical behavior of a cubic-lattice 3D Ising model for systems with quenched disorder. Numerical results are presented for the spin concentrations of p = 1.0, 0.95, 0.9, 0.8, 0.6 on L × L × L lattices with L = 20–60 under periodic boundary conditions. The critical temperature is determined by the Binder cumulant method. A finite-size scaling technique is used to calculate the static critical exponents α, β, γ, and ν (for specific heat, susceptibility, magnetization, and correlation length, respectively) in the range of p under study. Universality classes of critical behavior are discussed for three-dimensional diluted systems.