Critical and multicritical O(n) models

Abstract

Soluble O( n) models on the square lattice are found via the Yang-Baxter equations. In a parameter space of three coupling constants a number of distinct soluble cases are found for each value of n. Some of these constitute critical or multicritical points in the phase diagram. For all solutions the free energy per spin can be determined using the Bethe Ansatz. By studying the finite size corrections at the critical points, the critical exponents and the central charge can be found, in some cases analytically, and failing that, numerically by extrapolation of exact results for finite size systems.