The phase structure of the generalized Yang-Mills theories is studied, and it is shown that almost always, it is of the third order. As a specific example, it is shown that all of the models with the interaction Sigma (j)(n(j) - j + N)(2k) exhibit third order phase transition (n(j) is the length of the jth 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 Sigma (J)(n(j) - j + N)(2) + g Sigma (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. (C) 2001 Elsevier Science B.V. All rights reserved. [References: 18]
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