Critical properties of the Izergin-Korepin and solvable O(n) models and their related quantum spin chains

The central charge of the Izergin-Korepin model the corresponding quantum spin chain, and the O⁽ⁿ⁾ model is calculated analytically via the Bethe ansatz. The calculation extends a technique recently developed for the Zamolodchikov-Fateev model. In addition critical exponents and the central charge for these models are obtained from numerical solutions of Bethe ansatz equations for finite systems. As a physical application the authors find the exponents v=12/23 and gamma =53/46 for the Theta -transition of polymers in two dimensions.