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.

中文翻译：

---

关于有限正弦-戈登环的基态能量

描述了有限圆中正弦-戈登模型的基态能量的 Casimir 标度函数已经在排斥和吸引状态下进行了分析和数值研究。通过 Destri-de Vega 非线性积分方程的迭代求解，对耦合常数的几个值处的标度函数进行了数值计算。Casimir标度函数的紫外渐近性是通过这些方程的微扰解计算的，并通过微扰共形场理论技术，并与数值结果进行了比较。