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Journal of Superconductivity and Novel Magnetism

Phase Transitions and Critical Behavior in the Two-Dimensional Weakly Diluted 4-State Potts Model

A.K. Murtazaev, Albert Babaevich Babaev, M. A. Babaev

Published Aug 1, 2026• 0 citations
Publisher
DOI
10.1007/s10948-026-07235-3

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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 .
Abstract The thermodynamic properties and phase transitions in the two-dimensional weakly diluted Potts model with the number of spin states q=4 were studied by the Monte Carlo method. Systems with linear dimensions L×L = N, L=10–160 are considered. Using the fourth order Binder cumulant method, critical temperatures were calculated for spin systems with a spin concentration p=1.0 and 0.90. Critical indices are calculated on the basis of the theory of finite-size scaling. The universality of the critical behavior of two-dimensional disordered systems is discussed.