Exact solution of the Perk-Schultz model.

Abstract

In the Perk-Schultz vertex model links can have n+1 different colors and the weights are ferroelectric or antiferroelectric depending on a discrete parameter ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}}$=\ifmmode\pm\else\textpm\fi{}1 (1\ensuremath{\le}a\ensuremath{\le}n). We compute the exact ground-state spins and find ferrielectric behavior for general signs ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}}$. The exact free energy and excitation spectrum are found as well as the finite-size corrections yielding the central charge and conformal dimensions. The scaling limit yields a quantum field theory whose mass spectrum and S matrix are explicitly obtained through the light-cone approach. The mass spectrum surprisingly depends on the anisotropy parameter and the signs ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}}$.