Star – Matrix Models

The star-matrix models are difficult to solve due to the multiple powers of the Vandermonde determinants in the partition function. We apply to these models a modified Q-matrix approach and we get results consistent with those obtained by other methods.As examples we study the inhomogenous gaussian model on Bethe tree and matrix q-Potts-like model. For the last model in the special cases q = 2 and q = 3, we write down explicit formulas which determinate the critical behaviour of the system.For q = 2 we argue that the critical behaviour is indeed that of the Ising model on the φ 3 lattice.