Finite Temperature Properties of SO(3) Lattice Gauge Theories and their implications for the continuum limit

It is shown that $SO(3)$ lattice gauge theory on finite size lattices has metastable states related to the ground states of both the bulk transition and the finite temperature transition. The Polyakov line variable in the adjoint representation of $SU(2)$ is used to trace the origin of these metastable states. It is also argued that a second order finite temperature transition in the continuum theory is not inconsistent with the first order transition in $SO(3)$ lattice gauge theory and the absence of a $Z(2)$ global symmetry.