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Journal of Physics A Mathematical and General

Time continuous limit for the Baxter model

Valter L. Líbero, J. R. Drugowich de Felício

Published Aug 21, 1983• 4 citations
Publisher

Abstract

The authors obtain the associated Hamiltonian for the symmetric eight-vertex model by taking the time-continuous limit in an equivalent Ashkin-Teller (1943) model. The result is a Heisenberg Hamiltonian with coefficients J x , J y and J z identical to those found by Sutherland (1970) for choices of the parameters a, b, c and d that bring the model close to the transition. The change in the operators is accomplished explicitly, the relation between the crossover operator for the Ashkin-Teller model and the energy operator for the eight-vertex model being obtained in a transparent form.

DOI
10.1088/0305-4470/16/12/004

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The authors obtain the associated Hamiltonian for the symmetric eight-vertex model by taking the time-continuous limit in an equivalent Ashkin-Teller (1943) model. The result is a Heisenberg Hamiltonian with coefficients J x , J y and J z identical to those found by Sutherland (1970) for choices of the parameters a, b, c and d that bring the model close to the transition. The change in the operators is accomplished explicitly, the relation between the crossover operator for the Ashkin-Teller model and the energy operator for the eight-vertex model being obtained in a transparent form.
Nós obtemos o hamiltoniano associado ao modelo de oito vértices simétrico, tomando o limite de tempo contínuo em um modelo equivalente (modelo de Ashkin-Teller). O resultado é um hamiltoniano de Heisenberg com coeficientes Jx , Jy e Jz idênticos àqueles encontrados por Sutherland, na região crítica. A mudança nos operadores é acompanhada explicitamente e a relação entre o operador \"crossover\" do modelo de Ashkin-Teller e o operador energia do modelo de Baxter é obtida de forma transparente.
Nós obtemos o hamiltoniano associado ao modelo de oito vértices simétrico, tomando o limite de tempo contínuo em um modelo equivalente (modelo de Ashkin-Teller). O resultado é um hamiltoniano de Heisenberg com coeficientes Jx , Jy e Jz idênticos àqueles encontrados por Sutherland, na região crítica. A mudança nos operadores é acompanhada explicitamente e a relação entre o operador \\"crossover\\" do modelo de Ashkin-Teller e o operador energia do modelo de Baxter é obtida de forma transparente.
It is shown that Baxter's method when applied to the XXZ hamiltonian gives a set of eigenvectors and wavenumbers different from those of the familiar Bethe solution. In this limiting case of Baxter's results for the eight-vertex model the author finds that one of Baxter's parameters corresponds to the freedom of making arbitrary rotations about the z axis. It is suggested that for the general XXZ hamiltonian there may be a generalization of the ordinary z component of spin which would be conserved in addition to Baxter's quantum number.