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

Three-dimensional Z(N)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)Z(N) model for N=2,3,4,5,6,8N=2,3,4,5,6,8. Numerical computations are used to simulate vector models for N=2,3,4,5,6,8,13,20N=2,3,4,5,6,8,13,20 for lattices with linear extension up to L=96L=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>4N>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.