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Paper IPM / P / 6722  


Abstract:  
Using the auxiliary field representation of the simplicial chiral models on a (d1)dimensional simplex, the simplicial chiral models are generalized through replacing the term Tr(AA^{f}) in the Lagrangian of these models by an arbitrary class function of AA^{f}; V(AA^{f}). This is the same method used in defining the generalized twodimensional YangMills theories gYM_{2} from ordinary YM_{2}. We call these models, the "generalized simplicial chiral models". Using the results of the onelink integral over a U(N) matrix, the largeN saddlepoint equations for eigenvalue density function \ro (z) in the weak β > β_{c} and strong β < β_{c} regions are computed. In d=2, where the model is in some sense related to the gYM_{2} theory, the saddlepoint equations are solved for \ro (z) in the two regions, and the explicit value of critical point β_{c} is calculated for V(B)=TrB^{n}
(B=AA^{\dager}). For V(B)=TrB^{2},TrB^{3}, and TrB^{4}, 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.
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