STAR-MATRIX MODELS

The star-matrix models are difficult to solve due to the multiple powe rs of the Vandermonde determinants in the partition function. We apply to these models a modified Q-matrix aprpoach and we get results consi stent with those obtained by other methods. As examples we study the i nhomogeneous Gaussian model on Bethe tree and matrix q-Potts-like mode l. For the last model in the special cases q = 2 and q = 3, we write d own explicit formulas which determine the critical behavior of the sys tem. For q = 2 we argue that the critical behavior is indeed that of t he Ising model on the phi(3) lattice.