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| Paper IPM / P / 6722 |
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| Abstract: | |
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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(AAf) in the Lagrangian of these models by an arbitrary class function of AAf; V(AAf). This is the same method used in defining the generalized two-dimensional Yang-Mills theories gYM2 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 \ro (z) in the weak β > βc and strong β < βc regions are computed. In d=2, where the model is in some sense related to the gYM2 theory, the saddle-point equations are solved for \ro (z) in the two regions, and the explicit value of critical point βc is calculated for V(B)=TrBn
(B=AA\dager). For V(B)=TrB2,TrB3, 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.
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