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In two-dimensional Yang-Mills and generalized Yang-Mills theories for largegauge groups, there is a dominant representation determining the thermodynamiclimit of the system. This representation is characterized by a density thevalue of which should everywhere be between zero and one. This density itselfis determined through a saddle-point analysis. For some values of the parameterspace, this density exceeds one in some places. So one should modify it toobtain an acceptable density. This leads to the well-known Douglas-Kazakovphase transition. In generalized Yang-Mills theories, there are also regions inthe parameter space where somewhere this density becomes negative. Here too,one should modify the density so that it remains nonnegative. This leads toanother phase transition, different from the Douglas-Kazakov one. Here thegeneral structure of this phase transition is studied, and it is shown that theorder of this transition is typically three. Using carefully-chosen parameters,however, it is possible to construct models with phase-transition orders notequal to three. A class of these non-typical models are also studied.Comment: 11 pages, accepted for publication in Eur. Phys. J.

Non-Douglas–Kazakov phase transition of two-dimensional generalized Yang–Mills theories