The phase transitions in 2D Z(N) vector models for N>4

Abstract

We investigate both analytically and numerically the renormalization group equations in 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, 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, 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.

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

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• The Binder Cumulant at the Kosterlitz-Thouless Transition
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Cited by in corpus (16)

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• Monte Carlo study of duality and the Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional $q$-state clock model in flow representations
• Logarithmic finite-size scaling correction to the leading Fisher zeros in the p-state clock model: A higher-order tensor renormalization group study
• Ordering kinetics in q-state clock model: scaling properties and growth laws
• Clock model interpolation and symmetry breaking in O(2) models
• Phase transitions of the five-state clock model on the square lattice
• Deconfinement transition and localization of Dirac modes in finite-temperature ${\mathbb{Z}}_3$ gauge theory on the lattice
• Quasi Long Range Order and Vortex Lattice in the Three State Potts Model
• Phase transitions in strongly coupled 3d Z(N) lattice gauge theories at finite temperature
• Phase structure of 3D Z(N) lattice gauge theories at finite temperature
• Phase structure of 3D Z(N) lattice gauge theories at finite temperature: large-N and continuum limits
• BKT phase transitions in two-dimensional non-Abelian spin models
• Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions