Exact solution of the Perk-Schultz model

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 ${\mathrm{\epsilon }}_{\mathit{a}}$=±1 (1≤a≤n). We compute the exact ground-state spins and find ferrielectric behavior for general signs ${\mathrm{\epsilon }}_{\mathit{a}}$. 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 ${\mathrm{\epsilon }}_{\mathit{a}}$.