Generalized simplicial chiral models Original Research Article

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†) in the Lagrangian of these models by an arbitrary class function of AA†; V(AA†). 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 ρ(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 ρ(z) in the two regions, and the explicit value of critical point βc is calculated for V(B)=Tr Bn (B=AA†). For V(B)=Tr B2,Tr B3, 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.