Is there a third-order phase transition in quenched QCD?
  We discuss the connection between the contributions of large field configurations and the large order behavior of perturbation theory. For quenched QCD, the sensitivity of the average plaquette to a removal of large field configurations has a narrow peak near beta=5.6. Various analysis of the order 10 weak coupling series for the plaquette give robust indications for a singularity in the third derivative of the free energy (second derivative of the plaquette) with respect to beta, near beta = 5.7. We report results of numerical calculations. The peak in the third derivative of the free energy present on 4^4 lattices disappears if the size of the lattice is increased isotropically up to a 10^4 lattice. On the other hand, on 4xL^3 lattices, it persists when L increases. The location of the peak coincides with the onset of a non-zero average for the Polyakov loop and seems related to the finite temperature transition. We also discuss the discrepancy between the perturbative series and the numerical values of the plaquette. 
L. Li and Y. Meurice