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General Vertex Model: Exact Results and Finite - Analyses

Xue-Ning Wu

Published Jan 1, 1990• 0 citations
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Vertex models and related algebras

Series on advances in statistical mechanics•Feb 1, 1991•0 citations
A seven-vertex model on the honeycomb lattice is solved exactly by the Bethe ansatz method. The vertex model is equivalent to the critical O(n) model on the honeycomb lattice. The equivalence is made exact for lattices wrapped on a cylinder with one finite and one infinite direction, by the introduction of a seam into the vertex model. Thus asymptotic finite-size amplitudes of the critical O(n) model are obtained exactly. Applications of the theory of conformal invariance, which relate these amplitudes to the central charge and critical exponents, confirm the existing results and conjectures for these quantities. The finite-size amplitude corresponding to the temperature exponent was not obtained from the exact solution. However, this amplitude was accurately determined from numerical finite-size results obtained by the transfer-matrix method. This result also agrees with recent predictions.
Exact results are obtained for a square lattice fifteen-vertex model and related O(n) model recently proposed by Nienhuis (1990). The partition function per site and finite-size corrections are obtained, along with the critical exponents via the Temperley-Lieb equivalent six-vertex model. The exact exponents nu = 4 / 7 and gamma = 6 / 7 follow in the limit n=0 for even system sizes. Odd system sizes are also discussed. The fifteen-vertex model is also the vertex formulation of the anisotropic, or q-deformed, spin-1 biquadratic model.