Generalized simplicial chiral models

Using the auxiliary field representation of the simplicial chiral models on a (d - 1)-dimensional simplex, the simplicial chiral models are generalized through replacing the term Tr(AA dagger) in the Lagrangian of these models by an arbitrary class function of AA dagger; V(AA dagger). This is the same method used in defining the generalized two-dimensional Yang-Mills theories (gYM(2)) from ordinary YM2. We call these models the ''generalized simplicial chiral models''. Using the results of the one-link integral over a U(N) matrix, the large-N saddle-point equations for eigenvalue density function rho(z) in the weak (beta > beta(c)) and strong (beta < beta(c)) regions are computed. In d = 2, where the model is in some sense related to the gYM(2) theory, the saddle-point equations are solved for rho(z) in the two regions, and the explicit value of critical point beta(c) is calculated for V(B) = Tr B-n (B = AA dagger). For V(B) = Tr B-2,Tr B-3, and TrB4, the critical behaviour of the model at d = 2 is studied, and by calculating the internal energy, it is shown that these models have a third order phase transition. (C) 2000 Elsevier Science B.V. All rights reserved.