Properties of linear integral equations related to the six-vertex model with disorder parameter

Abstract

One of the key steps in recent work on the correlation functions of the XXZ chain was to regularize the underlying six-vertex model by a disorder parameter $\alpha$. For the regularized model it was shown that all static correlation functions are polynomials in only two functions. It was further shown that these two functions can be written as contour integrals involving the solutions of a certain type of linear and non-linear integral equations. The linear integral equations depend parametrically on $\alpha$ and generalize linear integral equations known from the study of the bulk thermodynamic properties of the model. In this note we consider the generalized dressed charge and a generalized magnetization density. We express the generalized dressed charge as a linear combination of two quotients of $Q$-functions, the solutions of Baxter's $t$-$Q$-equation. With this result we give a new proof of a lemma on the asymptotics of the generalized magnetization density as a function of the spectral parameter.

10 pages, latex, needs ws-procs9x6.cls, dedicated to Prof. Tetsuji Miwa on the occasion of his 60th birthday; v2 minor corrections; v3 fonts replaced

References in corpus (6)

• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Fermionic structure in the sine-Gordon model: form factors and null-vectors
• Completeness of a fermionic basis in the homogeneous XXZ model
• Quantum spin chains at finite temperatures
• Fermionic screening operators in the sine-Gordon model
• Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States

Cited by in corpus (2)

• Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
• Properties of linear integral equations related to the six-vertex model with disorder parameter II