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

Abstract

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