High-temperature expansion along the self-dual line of three-dimensionalZ(2)spin-gauge theory

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.