Abstract
The formalism developed by Sarker and Krumhansl (1981) for the investigation of a phi 4 system with long-range interactions of the Kac-Baker type is extended to the study of the thermodynamical properties of a sine-Gordon (SG) and a double sine-Gordon (DSG) chain with long-range interactions. This extension enlarges the class of non-linear systems which can support kink solutions. In the continuum limit, the author deduces compact analytical expressions for the SG-kink solutions and the DSG-kink solutions as well as for their associated energies. Both the kink solutions and the kink energies depend on the kink width. As the interaction range increases it is found that the kink width and the kink energy increase indefinitely-the kinks disappear. Consequently one can consider the kinks as 'elementary excitations' only in the limit of not too large interaction ranges, when they will destroy long-range order in the system. For this limit he determined the phonon and kink contribution to the free-energy density at low temperatures. For the infinite interaction range limit he has found that the two systems studied undergo a second-order phase transition. The critical behaviour is-as expected-similar to that of the phi 4 system with long-range interactions.