ON THE PHASE-DIAGRAM OF THE SU(2) ADJOINT HIGGS-MODEL IN 2-DIMENSIONS(1)

The phase diagram is investigated for SU(2) lattice gauge theory in d = 3, coupled to adjoint scalars. For small values of the quartic scala r coupling, lambda, the transition separating Higgs and confinement ph ases is found to be first-order, in agreement with earlier work by Nad karni. 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 cr itical point at which the scalar mass vanishes. The photon mass and co nfining string tension are measured and are found to be negligibly sma ll in the Higgs phase. This is correlated with the very small density of magnetic monopoles in the Higgs phase. The string tension and photo n mass rise rapidly as the crossover is traversed towards the symmetri c phase. (C) 1997 Elsevier Science B.V.