Solvable hierarchy of cyclic solid-on-solid lattice models

Abstract

A hierarchy of L-state cyclic solid-on-solid lattice models, related to the Andrews-Baxter-Forrester solid-on-solid models, is solved exactly. In addition to the usual anisotropy parameter (spectral parameter) u and the temperaturelike variable (elliptic nome) p, the exact solution admits a phase angle ${\mathrm{w}}_{0}$ that interpolates between heights. Results for the free energy and local height probabilities are obtained. The exact solution exhibits first-order coexistence manifolds which coalesce at the multicritical point (p=0). For L=3, our results extend Baxter's results on the three colorings of the square lattice.