On the phase diagram of the SU(2) adjoint Higgs model in 2+1 dimensions

The phase diagram is investigated for SU(2) lattice gauge theory in d = 3, coupled to adjoint scalars. For small values of the quartic scalar coupling, lambda, the transition separating Higgs and confinement phases is found to be first-order, in agreement with earlier work by Nadkarni. The surface of second-order transitions conjectured by Nadkarni, however, is shown instead to correspond to crossover behaviour. This conclusion is based on a finite size analysis of the scalar mass and susceptibility. The nature of the phase transition at the termination of first-order behaviour is investigated and we find evidence for a critical point at which the scalar mass vanishes. The photon mass and confining string tension are measured and are found to be negligibly small in the Higgs phase. This is correlated with the very small density of magnetic monopoles in the Higgs phase. The string tension and photon mass rise rapidly as the crossover is traversed towards the symmetric phase. (C) 1997 Elsevier Science B.V.