Phase transitions in two-dimensionalZ(N)vector models forN>4

2011/12/31 by O. Borisenko, V. Chelnokov, G. Cortese +7
Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Condensed matter physics #Critical exponent #Critical phenomena #Markov Chains and Monte Carlo Methods #Mathematical physics #Mathematics #Monte Carlo method #Phase transition #Physics #Renormalization group #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat

paper · pdf · doi:10.1103/physreve.85.021114

19 pages, 8 figures, 10 tables; version to appear on Phys. Rev. E

arxiv created 2012/01/28 · openalex publication_date 2012/02/09 · arxiv updated 2013/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

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