Large-N limit of the generalized two-dimensional Yang-Mills theories

Using the standard saddle-point method, we find an explicit relation for the large-N limit of the free energy of an arbitrary generalized 2D Yang-Mills theory in the weak (A < A(c)) region. In the strong (A > A(c)) region, we investigate carefully the specific fourth Casimir theory, and show that the ordinary integral equation of the density function is not adequate to find the solution. There exist, however, another equation which restricts the parameters. So one can find the free energy in the strong region and show that the theory has a third-order phase transition. (C) 1998 Elsevier Science B.V.