Integrable O(n) model on the honeycomb lattice via reflection matrices : Surface critical behaviour

We study the $O(n)$ loop model on the honeycomb lattice with open boundary conditions. Reflection matrices for the underlying Izergin-Korepin $R$-matrix lead to three inequivalent sets of integrable boundary weights. One set, which has previously been considered, gives rise to the ordinary surface transition. The other two sets correspond respectively to the special surface transition and the mixed ordinary-special transition. We analyse the Bethe ansatz equations derived for these integrable cases and obtain the surface energies together with the central charges and scaling dimensions characterizing the corresponding phase transitions.