SU(N) gauge theories near Tc

We study the deconfinement phase transition in SU(N) gauge theories for N=2,3,4,6,8. The transition is first order for N greater than or equal to 3, with the strength increasing as N increases. We extrapolate T-c/rootsigma to the continuum limit for each N, and observe a rapid approach to the large N limit. As N increases the phase transition becomes clear-cut on smaller spatial volumes, indicating the absence of (non-singular) finite volume corrections at N = infinity - reminiscent of large N reduction. The observed rapid increase of the inter-phase surface tension with N may indicate that for N = infinity the deconfinement transition cannot, in practise, occur.