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Second-Order Phase Transition Induced by the Quenched Random Dilution in 3D

Katarina Uzelac, A. Aničić, O. S. Barišić

Published Jan 1, 1999• 0 citations
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Abstract

The eect of the quenched random dilution on the ferromagnetic transitions, in particular, the conversion from the rst- to second-order transition is discussed. The new results are presented for the diluted three-dimensional three-state Potts model. The critical exponents of the disorder-induced second-order phase transition are derived by the nite-size scaling analysis of the moments of the energy and the largest cluster, obtained from the Monte Carlo simulations. PACS numbers: 05.50.+q, 64.60.Cn UDC 536.764

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The eect of the quenched random dilution on the ferromagnetic transitions, in particular, the conversion from the rst- to second-order transition is discussed. The new results are presented for the diluted three-dimensional three-state Potts model. The critical exponents of the disorder-induced second-order phase transition are derived by the nite-size scaling analysis of the moments of the energy and the largest cluster, obtained from the Monte Carlo simulations. PACS numbers: 05.50.+q, 64.60.Cn UDC 536.764
Monte Carlo simulations are performed to analyze phase transitions in three-dimensional systems described by the 3-state Potts model with nonmagnetic impurities. Numerical results are presented for systems with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 on lattices of size L varying between 20 and 44. Binder’s cumulant analysis shows that the introduction of quenched disorder in the form of non-magnetic impurities induces a crossover from first-order to second-order phase transition. The finite-size scaling method is used to calculate the static critical exponents α, γ, β, and ν for specific heat, susceptibility, magnetization, and correlation length, respectively.
We study by extensive Monte Carlo simulations the effect of random bond dilution on the phase transition of the three-dimensional four-state Potts model that is known to exhibit a strong first-order transition in the pure case. The phase diagram in the dilution-temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes. In the strongly disordered regime, numerical evidence for softening to a second-order transition induced by randomness is given. Here a large-scale finite-size scaling analysis, made difficult due to strong crossover effects presumably caused by the percolation fixed point, is performed.
The effect of quenched nonmagnetic impurities on phase transitions in the three-dimensional Potts model with the number of spin states q=3 is studied using the Wolff single-cluster algorithm of the Monte Carlo method. By the method of fourth-order Binder cumulants, it is demonstrated that the second-order phase transition occurs in the model under study at spin concentrations p=0.9, 0.8, 0.7, and 0.65, while the first-order phase transition is observed in the pure model (p=1.0). The static critical exponents (CEs) α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length) are calculated based on the finite-size scaling theory.
In this report we give an overview on recent results obtained from extensive Monte Carlo (MC) computer simulations of the 3D 2-state (Ising) and 4-state Potts models with bond-dilution. The motivation to study the 4-state Potts model derives from the fact that, in the pure case, this model is known to exhibit a fairly strong first-order transition, such that a disorder-induced softening to a second-order transition would give clear support of the theoretical expectations. Modeling the disorder by bond-dilution enables in the Ising case a test of the expected universality with respect to the type of disorder. Furthermore, for both models this choice facilitates a quantitative comparison with recent high-temperature series expansions for general random-bond q-state Potts models.
Three-state Potts ferromagnets on the simple cubic lattice in random fields are studied by extensive Monte Carlo simulation. The implications of the possible hyperscaling violation to finite-size scaling are discussed. Evidence for a second-order transition is obtained, as well as rough estimates for critical exponents. A qualitative phase diagram is proposed compatible with the predictions of Blankschtein et al. on the random field-induced shift of the tricritical curve q = q c ( d ) in the plane of variables dimensionality d and number of states q .