THE O(N) MODEL ON THE TRIANGULAR LATTICE

To find critical points of O(n) models on the triangular lattice we ap ply two methods. First we investigate the Yang-Baxter equations on the triangular lattice. We find only solvable points directly related to those for the square lattice. Second we construct intersections with t he Potts model. This yields eight branches of critical points, paramet rized by n. We establish the equivalence of these branches with the kn own critical points of the O(n) model on the square lattice. Transfer- matrix calculations are performed to obtain the conformal anomaly and the thermal exponent of these branches. These results include a numeri cal analysis of a q = 3 Potts tricritical point. We find analytic rela tions between Potts and O(n) models, as well as among O(n) models with different values of n, and among Potts models with different values o f q.