Sine-Gordon model at finite temperature: The method of random surfaces

We study the sine-Gordon quantum field theory at finite temperature by generalizing the method of random surfaces to compute the free energy and one-point functions of exponential operators nonperturbatively. Focusing on the gapped phase of the sine-Gordon model, we demonstrate the method's accuracy by comparing our results to the predictions of other methods and to exact results in the thermodynamic limit. We find excellent agreement between the method of random surfaces and other approaches when the temperature is not too small with respect to the mass gap. Extending the method to more general problems in strongly interacting one-dimensional quantum systems is discussed.