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

TL;DR

This paper investigates the phase transitions in two-dimensional generalized Yang--Mills theories, revealing that most models exhibit third order phase transitions, with some exceptions showing different transition orders.

Contribution

It provides a comprehensive analysis of the phase structure in generalized Yang--Mills theories, identifying conditions for third order and other phase transition orders.

Findings

Most models exhibit third order phase transitions.

Certain models show a transition of order 5/2 at specific parameters.

The transition order depends on the form of the interaction term.

Abstract

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 $\sum_j (n_j-j+N)^{2k}$ exhibit third order phase transition. ($n_j$ 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 $\sum_j (n_j-j+N)^2+g\sum_j (n_j-j+N)^{4}$ exhibits a third order phase transition, except for $g=27\pi^2/256$, where the order of the transition is 5/2.