Correlation length and order of the deconfining phase transition

We analyze SU(2) and SU(3) lattice gauge theory on $L_t$×$L^2$∞ lattices ($L_t$≤L). By ${\beta }_c$ 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’)→${\beta }_c$ for L’→∞], the correlation length ξ scales ∼L/L’ for second- and first-order transitions (ξ=1/$E_1$ with $E_1$ 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 ($L_t$=4) support a second-order transition for SU(2), but not for SU(3).