Low-temperature soliton-gas phenomenology for sine-Gordon systems with a winding-number density

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Abstract
The ideal-kink-gas phenomenology of Currie, Krumhansl, Bishop, and Trullinger is extended to include the case of nonzero winding-number density in sine-Gordon systems. By considering kinks and antikinks to be substates of a single type of "particle" and taking into account the renormalization of the kink energy due to phase-shift interactions between kinks and phonons, simple expressions are obtained for the low-temperature, average kink and winding-number densities as a function of the winding-number potential. The results agree with the exact transfer-operator results of Currie, Fogel, and Palmer.