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arXiv · 1310.5997

Critical behavior of 3D Z(N) lattice gauge theories at zero temperature

O. Borisenko·V. Chelnokov·G. Cortese·M. Gravina·A. Papa·I. Surzhikov
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Abstract

Three-dimensional $Z(N)$ lattice gauge theories at zero temperature are studied for various values of $N$. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized $Z(N)$ model for $N=2,3,4,5,6,8$. Numerical computations are used to simulate vector models for $N=2,3,4,5,6,8,13,20$ for lattices with linear extension up to $L=96$. We locate the critical points of phase transitions and establish their scaling with $N$. The values of the critical indices indicate that the models with $N>4$ belong to the universality class of the three-dimensional $XY$ model. However, the exponent $α$ derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle. We also demonstrate the existence of a rotationally symmetric region within the ordered phase for all $N\geq 5$ at least in the finite volume.

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O. Borisenko, V. Chelnokov, G. Cortese, M. Gravina, A. Papa, I. Surzhikov. 2013-10-22. Critical behavior of 3D Z(N) lattice gauge theories at zero temperature. https://doi.org/10.1016/j.nuclphysb.2013.12.003

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