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Using Monte Carlo techniques, we study the thermodynamics of four-dimensional Euclidean lattice gauge theories, with gauge groups Z₍ and U (1). For N4 the models exhibit a single first-order phase transition, while for N5 we observe two transitions of higher order. As N increases, one of these transitions moves toward zero temperature, whereas the other remains at finite temperature and survives in the U (1) limit. The behavior of the Wilson loop factor is also analyzed for the Z₂ and Z₆ models.
Creutz et al. (Mon,) studied this question.