Classical statistical mechanics of one-dimensional polykink systems

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Abstract
The phenomenological ideal-kink-gas theory recently developed by Currie, Krumhansl, Bishop, and Trullinger for the low-temperature statistical mechanics of one-dimensional, nonlinear, Klein-Gordon chains is extended and modified to treat systems capable of supporting more than one type of kink excitation. In particular, we consider a general class of local potentials that are doubly periodic, such as the double-sine-Gordon and doubly-periodic-quadratic cases, and support two different types of kinks having different creation energies. By taking into account topological restrictions on the sequencing of these two types of kinks (and their antikinks) along the chain, we find that the ideal-gas theory precisely reproduces results obtainable by the transfer-operator method. In addition, we present formulas for the low-temperature densities of kinks that depend only on quantities obtainable directly from the local potential and not on explicit knowledge of the waveforms of the kinks or their small oscillations.