Three-dimensional 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 model for . Numerical computations are used to simulate vector models for for lattices with linear extension up to . 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 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.
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