Second order transitions in Z(2) gauge theory in four dimensions

Abstract

I study the four-dimensional Z(2) gauge theory with asymmetric couplings ( β 1 for the xy, xz, xt plaquettes and β 2 for the yz, yt, zt plaquettes) by Monte Carlo simulation. A rich phase structure is found in the β 1, β 2 plane. In particular, there are lines of second order transitions that meet in a tri-critical point at which a four-dimensional Lorentz invariant continuum limit might exist. Further, the limit β 1 → ∞, β 2 → 0 for which the hamiltonian theory is obtained, is found to be the end-point of a line of first order transitions. The prediction therefore is that the hamiltonian formulation of this theory has a second order phase transition with infinite correlation length.