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

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.

14 pages, LaTex, one paragraph is added to introduction section, to describe the 5/2 phase transition, accepted for publication in Nucl. Phys. B (2001)

References in corpus (2)

• Uniqueness of the minimum of the free energy of the 2D Yang-Mills theory at large N
• Phase structure of the generalized two dimensional Yang-Mills theories on sphere

Cited by in corpus (9)

• Phase transitions in q-deformed 2d Yang-Mills theory and topological strings
• Large-N limit of the two-dimensoinal Yang-Mills theory on surfaces with boundaries
• Large-N behavior of the Wilson loops of generalized two-dimensional Yang-Mills theories
• More on Phase Structure of Nonlocal 2D Generalized Yang-Mills Theories (nlgYM${}_2$'s)
• Phase transitions of Large-N two-dimensional Yang-Mills and generalized Yang-Mills theories in the double scaling limit
• Phase structure of the quartic-cubic generalized two dimensional Yang Mills U(N) on the sphere
• Non-Douglas-Kazakov phase transition of two-dimensional generalized Yang-Mills theories
• 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