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arXiv:1112.3604 · Physical Review E

Phase transitions in two-dimensional Z(N) vector models for N>4

Oleg Borisenko, V. Chelnokov, Gennaro Cortese, Roberto Fiore A, Mario Gravina, Alessandro Papa

Published Feb 9, 2012• 20 citations
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Abstract

We investigate both analytically and numerically the renormalization group equations in two-dimensional (2D) Z(N) vector models. The position of the critical points of the two phase transitions for N>4 is established and the critical index ν is computed. For N=7 and 17 the critical points are located by Monte Carlo simulations, and some of the corresponding critical indices are determined. The behavior of the helicity modulus is studied for N=5, 7, and 17. Using these and other available Monte Carlo data we discuss the scaling of the critical points with N and some other open theoretical problems.

DOI
10.1103/physreve.85.021114

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We investigate both analytically and numerically the renormalization group equations in two-dimensional (2D) Z(N) vector models. The position of the critical points of the two phase transitions for N>4 is established and the critical index ν is computed. For N=7 and 17 the critical points are located by Monte Carlo simulations, and some of the corresponding critical indices are determined. The behavior of the helicity modulus is studied for N=5, 7, and 17. Using these and other available Monte Carlo data we discuss the scaling of the critical points with N and some other open theoretical problems.
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The Monte Carlo method is used to study phase transitions in the two-dimensional Potts model with the number of states spin q=3 on square and hexagonal lattices. Considered systems with linear dimensions Lx L=N, L=21/102. The obtained numerical data indicate that in the considered In the Potts model, a second-order phase transition is observed in accordance with the analytical theory. The Binder cumulants method of the fourth order determines the values of the critical points of the Potts model on different lattices. Keywords: Phase transitions, Potts model, Monte Carlo, thermodynamic parameters, critical temperature.