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Quantum-statistical phonon free energy of the one-dimensional since-Gordon system is calculated perturbationally with respect to the coupling constant. Its classical limit agrees completely with the phonon terms with anharmonic effects obtained by the transfer integral method. The free energy associated with the n =2 breather is shown to be a part of such anharmonic phonon terms.
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Takayama et al. (1981) studied this question.
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