On the phase structure of two-dimensional generalized Yang-Mills theories

The phase structure of the generalized Yang-Mills theories is studied, and it is shown that almost always, it is of the third order. As a specific exa mple, it is shown that all of the models with the interaction Sigma (j)(n(j ) - j + N)(2k) exhibit third order phase transition (n(j) is the length of the jth row of the Yang tableau corresponding to U(N).) The special cases w here the transition is not of the third order are also considered and, as a specific example, it is shown that the model Sigma (J)(n(j) - j + N)(2) g Sigma (j)(n(j) - j + N)(4) exhibits a third order phase transition, excep t for g = 27 pi (2)/256, where the order of the transition is 5/2. (C) 2001 Elsevier Science B.V. All rights reserved.