Ising spin gauge theory at upper marginal dimensionality for spin glasses

Abstract

The Ising spin gauge theory along its line of vanishing unit Wilson loop has been proposed as a model for spin glasses. The authors have performed Monte Carlo simulations to determine the phase diagram of this theory in six dimensions, the upper marginal dimensionality attributed to true spin glasses. As in three and four dimensions, the contour of vanishing Wilson loops does not meet a transition line for finite values of either the gauge or spin-spin coupling constant. It is concluded that either the gauge theory analogy is incorrect or the upper marginal dimension of spin glasses is not six.