Statistical Mechanics of the 1D Sine-Gordon System. II. Transfer Integral Analysis in the Intermediate Temperature Region

We study thermodynamical properties of the classical one-dimensional sine-Gordon system in finite temperatures comparable with and less than the soliton energy E _S by means of the transfer integral method. Comparing its analytical solutions with its exact results obtained numerically, we show that the ideal soliton gas phenomenology breaks down at the temperature region around \(k_{\text{B}}T{\gtrsim}0.2E_{\text{S}}\), above which the interaction between solitons plays an appreciable role even quantitatively.