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arXiv:1307.0198

Spontaneous polarization of spin 1 analogue of the eight-vertex model

Yas-Hiro Quano

Published Jun 30, 2013• 0 citations
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Abstract

The spin 1 analogue of the eight-vertex model is considered on the basis of free field representations of vertex operators in the 2 × 2-fold fusion SOS model and vertex-face transformation. The spontaneous polarization of the model is obtained in terms of one-fold integral formula. Some limiting cases are discussed in order to examine the validity of the formula. Furthermore, we also present the integral formulae of the one-point function for the inhomogeneous twenty-one-vertex model.

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The spin 1 analogue of the eight-vertex model is considered on the basis of free field representations of vertex operators in the 2 × 2-fold fusion SOS model and vertex-face transformation. The spontaneous polarization of the model is obtained in terms of one-fold integral formula. Some limiting cases are discussed in order to examine the validity of the formula. Furthermore, we also present the integral formulae of the one-point function for the inhomogeneous twenty-one-vertex model.
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Belavin's (ℤ/ n ℤ)-symmetric model is considered on the basis of bosonization of vertex operators in the A (1) n −1 model and vertex–face transformation. The corner transfer matrix (CTM) Hamiltonian of the (ℤ/ n ℤ)-symmetric model and tail operators are expressed in terms of bosonized vertex operators in the A (1) n −1 model. Correlation functions of the (ℤ/ n ℤ)-symmetric model can be obtained by using these objects, in principle. In particular, we calculate spontaneous polarization, which reproduces the result we obtained in 1993.