Thermodynamics of the magnetic double-sine-Gordon chain in the region of topological instability

A transfer-operator method and a perturbation approach are used to study the thermodynamics of the magnetic double-sine-Gordon chain near the point of topological instability, where the use of a dilute-gas approximation within the path-integral formalism fails. The low-temperature limit is investigated. A continuous crossover of magnetization between values calculated for low and higher external fields is obtained. In this region the magnetization is dominated by the sine-Gordon π-kink solitons, which are obtained at zero field.