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 {\it almost} always, it is of the third order. As a specific example, it is shown that all of the models with the interaction $\sum_j (n_j-j+N)^{2k}$exhibitthirdorderphasetransition\mathrm{.}($n_j$ 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 $\sum_j (n_j-j+N)^2+g\sum_j (n_j-j+N)^{4}$exhibitsathirdorderphasetransition,exceptfor$g=27\pi^2/256$, where the order of the transition is 5/2.