More on Phase Structure of Nonlocal 2D Generalized Yang-Mills Theories (nlgYM₂'s)

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We study the phase structure of nonlocal two dimensional generalized Yang - Mills theories (nlgYM₂) and it is shown that all order of ϕ²ᵏ 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 ϕ² + 2α/3ϕ³ model of nlgYM₂ has third order phase transition on any compact manifold with 1 < g < 1+ A|ηc|, and has no phase transition on sphere.