ar X iv : h ep - t h / 93 03 11 8 v 1 2 0 M ar 1 99 3 YCTP - P 44 - 92 December 1992 USC - 93 - 013 Fused Potts Models

Generalizing the mapping between the Potts model with nearest neighbour interaction and the six vertex model, we build a family of " fused Potts models " related to the spin k/2 Uqsu(2) invariant vertex model and quantum spin chain. These Potts models have still variables taking values 1,. .. , Q (√ Q = q + q −1) but they have a set of complicated multi spin interactions. The general technique to compute these interactions, the resulting lattice geometry, symmetries, and the detailed examples of k = 2, 3 are given. For Q > 4 spontaneous magnetizations are computed on the integrable first order phase transition line, generalizing Baxter's results for k = 1. For Q ≤ 4, we discuss the full phase diagram of the spin one (k = 2) anisotropic and Uqsu(2) invariant quantum spin chain (it reduces in the limit Q = 4 (q = 1) to the much studied phase diagram of the isotropic spin one quantum spin chain). Several critical lines and massless phases are exhibited. The appropriate generalization of the Valence Bond State method of Affleck et al. is worked out.