Year: 2005
Type: article
Abstract: 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 six-vertex model. We show that these eigenvalues satisfy a non-stationary Schrödinger 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.
Authors: Vladimir V Bazhanov, Vladimir V Mangazeev
Institution: Australian National University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2037711073