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

TL;DR

This paper investigates functions related to the six-vertex model and XXZ spin chain, showing how they can be derived from a master function satisfying specific functional and asymptotic conditions, enabling efficient high-temperature series calculations.

Contribution

It introduces a method to derive correlation-related functions from a master function using difference operators, simplifying high-temperature expansion calculations.

Findings

Functions can be obtained by acting with difference operators on a master function.

The master function is uniquely determined by a functional equation and asymptotic conditions.

The method provides an efficient scheme for high-temperature series expansions.

Abstract

We study certain functions arising in the context of the calculation of correlation functions of the XXZ spin chain and of integrable field theories related with various scaling limits of the underlying six-vertex model. We show that several of these functions that are related to linear integral equations can be obtained by acting with (deformed) difference operators on a master function $\Phi$. The latter is defined in terms of a functional equation and of its asymptotic behavior. Concentrating on the so-called temperature case we show that these conditions uniquely determine the high-temperature series expansions of the master function. This provides an efficient calculation scheme for the high-temperature expansions of the derived functions as well.