The phase diagram of $\mathrm{SO}\left(3\right)\mathrm{}$ lattice gauge theory is investigated by Monte Carlo techniques on both symmetric $N_{\sigma }^4$ and asymmetric $N_{\sigma }^3\times N_{\beta }$ lattices with a view (i) to understanding the relationship between the bulk transition and the deconfinement transition, and (ii) to resolving the current ambiguity about the nature of the high temperature phase. A number of tests, including an introduction of a magnetic field and measurement of different correlation functions in the phases with positive and negative values for the adjoint Polyakov line, $L_a,$ lead to the conclusion that the two phases correspond to the same physical state. Studies on lattices of different sizes reveal only one phase transition for this theory on all of them and it appears to have a deconfining nature.

• Received 12 November 1997

DOI:https://doi.org/10.1103/PhysRevD.57.6618