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 example, it is shown that all of the models with the interaction ∑ j (nj − j+N) exhibit third order phase transition. (nj is the length of the j-th row of the Yang tableau corresponding to U(N).) The special cases where the transition is not of the third order are also considered and, as a specific example, it is shown that the model ∑ j (nj −j+N) +g ∑ j (nj −j+N) 4 exhibits a third order phase transition, except for g = 27π/256, where the order of the transition is 5/2. PACS numbers: 11.10.Kk, 11.15.Pg, 11.15.Tk