Time continuous limit for the Baxter model

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 Jx, Jy and Jz 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.