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Experiments with a Gauge Invariant Ising System

Using Monte Carlo techniques, we evaluate the path integral for the four-dimensional lattice gauge theory with a Z/sub 2/ gauge group. The system exhibits a first-order transition. This is contrary to the implications of the approximate Migdal recursion relations but consistant with mean-field-theory arguments. Our ''data'' agree well with a low-temperature expansion and the exact duality between the high- and low-temperature phases.