Finite size effects in the SS-model: two component nonlinear integral equations

TL;DR

This paper derives nonlinear integral equations to accurately describe the finite size effects on the ground state energy of the O(4) nonlinear sigma model and extends these methods to the SS-model.

Contribution

It introduces a new set of nonlinear integral equations for the finite size effects in the SS-model, generalizing previous approaches for the O(4) sigma model.

Findings

Derived finite set of nonlinear integral equations for O(4) model

Modified kernel functions for SS-model finite size effects

Equations valid for arbitrary real couplings

Abstract

We derive a finite set of nonlinear integral equations for describing the finite size dependence of the ground state energy of the O(4) nonlinear sigma model. By modifying the kernel functions of these equations we propose nonlinear integral equations for the finite size effects in the SS-model. The equations are formulated in terms of two complex valued unknown functions and they are valid for arbitrary real values of the couplings.