More on Phase Structure of Nonlocal 2D Generalized Yang-Mills Theories (nlgYM$_2$'s)

TL;DR

This paper investigates the phase transitions in nonlocal 2D generalized Yang-Mills theories, revealing that phase transition orders depend on the manifold's genus and specific models, with some models exhibiting third-order transitions.

Contribution

It provides a detailed analysis of phase structures in nlgYM$_2$ theories, identifying conditions for phase transitions and their orders on different compact manifolds.

Findings

All $ ext{phi}^{2k}$ models have third-order phase transitions on the sphere.

The $ ext{phi}^2 + rac{2 ext{alpha}}{3} ext{phi}^3$ model exhibits third-order transitions on certain manifolds.

No phase transition occurs for this model on the sphere.

Abstract

We study the phase structure of nonlocal two dimensional generalized Yang - Mills theories (nlgYM$_2$) and it is shown that all order of $\phi^{2k}$ model of these theories has phase transition only on compact manifold with $g = 0$(on sphere), and the order of phase transition is 3. Also it is shown that the $\phi^2 + \frac{2\alpha}{3}\phi^3$ model of nlgYM$_2$ has third order phase transition on any compact manifold with $1 < g < 1+ \frac{\hat{A}}{|\eta_c|}$, and has no phase transition on sphere.