Eight-vertex model and non-stationary Lame equation

Details Eight-vertex model and non-stationary Lame equation Eight-vertex model and non-stationary Lame equation

2004-11-09

arxiv.org/abs/hep-th/0411094v2

J.Phys.A38:L145,2005

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX, minor misprints corrected, references added

Scientific paper

10.1088/0305-4470/38/8/L01

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 $\Delta=-1/2$ six-vertex model. We show that these eigenvalues satisfy a non-stationary Schrodinger equation with the time-dependent potential given by the Weierstrass elliptic P-function where the modular parameter $\tau$ 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 Painleve III equation.

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