Phase structure of the generalized two dimensional Yang-Mills theories on sphere

Abstract

We find a general expression for the free energy of $G(\varphi )={\varphi }^{2k}$ generalized 2D Yang-Mills theories in the strong ($A>A_c$) region at large $N$. We also show that in this region, the density function of Young tableau of these models is a three-cut problem. In the specific ${\varphi }^6$ model, we show that the theory has a third order phase transition, like ${\varphi }^2$ (YM_2) and ${\varphi }^4$ models. We have some comments for $k\ge 4$ cases. At the end, we study the phase structure of ${\varphi }^2+g{\varphi }^4$ model for $g\le A/4$ region.

13 pages, LaTex,the introduction section was changed,will be appeared in: Eur. Phys. J. C (1999)

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• Non-local 2D Generalized Yang-Mills theories on arbitrary surfaces with boundary
• Large-N limit of non-local 2D generalized Yang-Mills theories on non-orientable surface