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arXiv:cond-mat/9906195 · Physical review. B, Condensed matter

Critical behavior in the site-diluted three-dimensional three-state Potts model

H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, Giorgio Parisi A, Juan Jesus Ruiz-Lorenzo

Published Feb 1, 2000• 55 citations
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Abstract

We have studied numerically the effect of quenched site dilution on a weak first-order phase transition in three dimensions. We have simulated the site diluted three-states Potts model studying in detail the second-order region of its phase diagram. We have found that the $\ensuremath{\nu}$ exponent is compatible with the one of the three-dimensional diluted Ising model, whereas the $\ensuremath{\eta}$ exponent is definitely different.

DOI
10.1103/physrevb.61.3215

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We have studied numerically the effect of quenched site dilution on a weak first-order phase transition in three dimensions. We have simulated the site diluted three-states Potts model studying in detail the second-order region of its phase diagram. We have found that the \ensuremathν\ensuremath{\nu}\ensuremathν exponent is compatible with the one of the three-dimensional diluted Ising model, whereas the \ensuremathη\ensuremath{\eta}\ensuremathη exponent is definitely different.
The phase transitions and critical phenomena in three-dimensional (3D) site-diluted 3-and 4-state Potts models is investigated by Monte-Carlo method based on the highly efficient Wolff algorithm. The systems with linear sizesL=20-44 at spin concentrationsp=1.00, 0.95, 0.90, 0.80, 0.70, 0.65 are explored. The second-order phase transition is shown to occur in the three-dimensional 3-state Potts model with nonmagnetic impurities. In the 4-state Potts model there are observed first-order phase transitions in weakly diluted state, when the model is strongly diluted the first-order phase transitions change to the second-order one. On the basis of the finite-size scaling theory static critical exponents of specific heatα, susceptibilityγ, magnetizationβ, and exponent of correlation radiusνfor the systems under study are calculated.
We perform intensive numerical simulations of the three-dimensional site-diluted Ising antiferromagnet in a magnetic field at high values of the external applied field. Even if data for small lattice sizes are compatible with second-order criticality, the critical behavior of the system shows a crossover from second-order to first-order behavior for large system sizes, where signals of latent heat appear. We propose ``apparent'' critical exponents for the dependence of some observables on the lattice size for a generic (disordered) first-order phase transition.
Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations p=0.95 and 0.8 at criticality. In contrast to studies of the critical behavior of the pure systems by the short-time dynamics method, our investigations of site-diluted Ising model have revealed three stages of the dynamic evolution characterizing a crossover phenomenon from the critical behavior typical for the pure systems to behavior determined by the influence of disorder. The static and dynamic critical exponents are determined with the use of the corrections to scaling for systems starting separately from ordered and disordered initial states. The obtained values of the exponents demonstrate a universal behavior of weakly site-diluted Ising model in the critical region. The values of the exponents are compared to results of numerical simulations which have been obtained in various works and, also, with results of the renormalization-group description of this model.
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.
The static critical behavior of the three-dimensional weakly diluted Potts model with the state q = 3 on a simple cubic lattice has been investigated by the Monte Carlo method using the Wolff single-cluster algorithm. It is shown that at the spin concentrations p = 0.9 and 0.8 a second-order phase transition is observed in the three-dimensional weakly diluted Potts model with the state q = 3. On the basis of the finite-size scaling theory, we calculated the static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the correlation-length exponent v .