Abstract
We exploit the self-duality of the three-dimensional Ising spin-gauge theory to develop an eighth-order high-temperature expansion for the partition function along the self-dual line. This generates a high-temperature series for the gauge-invariant, nearest-neighbor spin-spin correlation function. A Pad\'e analysis of this series reveals a pole along the self-dual line. Recent Monte Carlo simulations indicate that this theory has a first-order self-dual line emerging from a triple point. We interpret the Pad\'e pole as a theoretical estimate of the end point of this self-dual line.
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