Eight-vertex model and non-stationary Lamé equation
نویسندگان
چکیده
We study the ground state eigenvalues of Baxter’s Q-operator for the eight-vertex model in a special case when it describes the off-critical deformation of the ∆ = − 1 2 six-vertex model. We show that these eigenvalues satisfy a non-stationary Schrodinger equation with the time-dependent potential given by the Weierstrass elliptic ℘-function where the modular parameter τ plays the role of (imaginary) time. In the scaling limit the equation transforms into a “non-stationary Mathieu equation” for the vacuum eigenvalues of the Q-operators in the finite-volume massive sine-Gordon model at the super-symmetric point, which is closely related to the theory of dilute polymers on a cylinder and the Painlevé III equation. email: [email protected] email: [email protected]
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