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

Abstract

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.

LaTeX, 29 pages, with 5 PostScript figures

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• Spectrum of transfer matrix for $U_q(B_n)$-invariant $A_{2n}^{(2)}$ open spin chain
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Cited by in corpus (11)

• Conformal Random Geometry
• Solutions of the reflection equation for face and vertex models associated with $A_n^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ and $A_n^{(2)}$
• On $A_{n-1}^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)},A_{2n}^{(2)},A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ Reflection $K$-Matrices
• Boundary Yang-Baxter equation in the RSOS/SOS representation
• Surveying the quantum group symmetries of integrable open spin chains
• Open su(4)-invariant spin ladder with boundary defects
• Surface operator content of the A_L face models
• Extraordinary transition in the two-dimensional O(n) model
• Statistical Mechanics of Confined Polymer Networks
• The ghost algebra and the dilute ghost algebra
• Fusion hierarchies, $T$-systems and $Y$-systems for the dilute $A_2^{(2)}$ loop models on a strip