The deconfining phase transition in D=2+1 SU(N) gauge theories

We study the deconfining transition of SU(N) gauge theories in 2+1 dimensions for N ranging between N=2 and N=8. We confirm that the transition is second order for N<4 and first order for N>4. For the more delicate case of SU(4) all our evidence points to the transition being weakly first order. After extrapolating to the continuum limit, we obtain a deconfining temperature that can be well fitted by Tc/sqrt(sigma) = 0.9026(23) + 0.880(43)/N^2 for all N.