The $\mathrm{SO}\left(3\right)\mathrm{}$ lattice gauge theory with a Villain form of action was investigated by Monte Carlo techniques on asymmetric lattices with $N_{\tau }=2\mathrm{}$ and 4, where $N_{\tau }$ is the number of sites in the temporal extent. Unlike the results for higher $N_{\tau },$ only one transition of second order was found for $N_{\tau }=2.\mathrm{}$ An extended action with an irrelevant term to suppress $Z_2$ monopoles enabled us to get a better view of the deconfinement transition as the effects of bulk transition could be suppressed as well. Although the action has no global $Z_2$-symmetry for the $\mathrm{SO}\left(3\right)\mathrm{}$ theory, unlike the $\mathrm{SU}\left(2\right)\mathrm{}$ theory at finite temperature, our study revealed a second order deconfinement transition, with properties similar to the deconfinement transition of $\mathrm{SU}\left(2\right).$

• Received 12 January 1999

DOI:https://doi.org/10.1103/PhysRevD.60.034505