Phase-diagram of the Frustrated Gauge-invariant Ising-model

The phase diagram of the Z (2) gauge-invariant Ising model is studied at negative gauge coupling in three dimensions. Exact procedures are applied to establish the ground states and find, at nonzero temperatures, the minima of the local mean-field free energy. The resulting phase diagram exhibits one unfrustrated and two frustrated phases, in good agreement with Monte Carlo results. The interpretation of the various phases in terms of a gas of random surfaces with free edges is also discussed