Variational method for the Z (2) gauge model.

Abstract

A variational method similar to the used for the Ising model is appiled to the Hamiltonian Z (2) lattice gauge theory in three dimensions. It is shown that the proposal of a gauge-invariant ground state leads to a transition in the Wilson loop integral from the area to the perimeter behavior for a value of the coupling constant close to the symmetry point produced to self-duality. The discontinuity wich appears in the variational perimeter gives strong evidence in favor of the first-order nature to what occurs for the two-dimensional model.