Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-03-20
Int.J.Mod.Phys.A8:5165-5234,1993
Physics
High Energy Physics
High Energy Physics - Theory
60 pages and 39 figures, uuencoded, tar, compressed Latex files, YCTP-P44-92,USC-93-013
Scientific paper
10.1142/S0217751X93002071
Generalizing the mapping between the Potts model with nearest neighbor interaction and six vertex model, we build a family of "fused Potts models" related to the spin $k/2$ ${\rm U}_{q}{\rm su}(2)$ invariant vertex model and quantum spin chain. These Potts model have still variables taking values $1,\ldots,Q$ ($\sqrt{Q}=q+q^{-1}$) 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 $Q\leq 4$, we discuss the full phase diagram of the spin one ($k=2$) anisotropic and ${\rm U}_{q}{\rm su}(2)$ 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 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.
Koo Wai Ming
Saleur Herbert
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