Second virial coefficients in soliton free energies

The low-temperature thermodynamics of a class of one-dimensional nonlinear Klein-Gordon systems (e.g., the sine-Gordon and the ${\phi }^4$ models) is studied by means of the transfer-integral method. A general formula for the lowest-order correction to the free energy due to the interaction between solitons is obtained. Physical interpretation of the result is given based on a simple soliton-gas picture.