On the ground-state energy of the finite sine-Gordon ring

TL;DR

This paper investigates the ground-state energy of the sine-Gordon model on a finite ring, combining analytical and numerical methods to understand its Casimir scaling function across different regimes.

Contribution

It provides a comprehensive analysis of the Casimir scaling function for the sine-Gordon model, including new numerical solutions and comparisons with perturbative and conformal field theory approaches.

Findings

Numerical solutions of the Destri-de Vega equations for various coupling constants.

Ultraviolet asymptotics matched with perturbative and conformal field theory results.

Consistent behavior of the Casimir scaling function in both repulsive and attractive regimes.

Abstract

The Casimir scaling function characterising the ground-state energy of the sine-Gordon model in a finite circle has been studied analytically and numerically both in the repulsive and attractive regimes. The numerical calculations of the scaling function at several values of the coupling constant were performed by the iterative solution of the Destri-de Vega nonlinear integral equations. The ultraviolet asymptotics of the Casimir scaling functions was calculated by perturbative solution of these equations, and by means of the perturbed conformal field-theory technique, and compared with numerical results.