TY - JOUR

T1 - Integrable vertex and loop models on the square lattice with open boundaries via reflection matrices

AU - Yung, C. M.

AU - Batchelor, M. T.

PY - 1995/2/13

Y1 - 1995/2/13

N2 - The procedure for obtaining integrable vertex models via reflection matrices on the square lattice with open boundaries is reviewed and explicitly carried out for a number of two- and three-state vertex models. These models include the six-vertex model, the 15-vertex A2(1) model and the 19-vertex models of Izergin-Korepin and Zamolodchikov-Fateev. In each case the eigenspectra is determined by application of either the algebraic or the analytic Bethe ansatz with inhomogeneities. With suitable choices of reflection matrices, these vertex models can be associated with integrable loop models on the same lattice. In general, the required choices do not coincide with those which lead to quantum-group-invariant spin chains. The exact solution of the integrable loop models - including an O(n) model on the square lattice with open boundaries - is of relevance to the surface critical behaviour of two-dimensional polymers.

AB - The procedure for obtaining integrable vertex models via reflection matrices on the square lattice with open boundaries is reviewed and explicitly carried out for a number of two- and three-state vertex models. These models include the six-vertex model, the 15-vertex A2(1) model and the 19-vertex models of Izergin-Korepin and Zamolodchikov-Fateev. In each case the eigenspectra is determined by application of either the algebraic or the analytic Bethe ansatz with inhomogeneities. With suitable choices of reflection matrices, these vertex models can be associated with integrable loop models on the same lattice. In general, the required choices do not coincide with those which lead to quantum-group-invariant spin chains. The exact solution of the integrable loop models - including an O(n) model on the square lattice with open boundaries - is of relevance to the surface critical behaviour of two-dimensional polymers.

UR - http://www.scopus.com/inward/record.url?scp=0001516681&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(94)00448-N

DO - 10.1016/0550-3213(94)00448-N

M3 - Article

AN - SCOPUS:0001516681

SN - 0550-3213

VL - 435

SP - 430

EP - 462

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -