Correlation length and order of the deconfining phase transition

We analyze SU(2) and SU(3) lattice gauge theory on Lₜ×{}L²{∞} lattices (Lₜ{≤}L). By βc we denote the critical coupling at L={∞}. In the neighborhood of the deconfining phase transition, at appropriately defined coupling constants {β}(L,L'), L>L' [with {β}(L,L'){→}βc for L'{→}{∞}], the correlation length {ξ} scales {~}L/L' for second- and first-order transitions ({ξ}=1/E₁ with E₁ the energy of one unit of 't Hooft electric flux). Linearization around the couplings {β}(L,L') allows the calculation of critical exponents. Numerical results (Lₜ=4) support a second-order transition for SU(2), but not for SU(3).