Temperature dependence of first lattice corrections to the free-energy of kinkcompacton-bearing systems

Abstract

The free-energy of discrete nonlinear Klein–Gordon (NKG) systems withanharmonic interparticle interactions is derived by means of the transfer integraloperator method, with the first lattice corrections and kink–kink interactionstaken into account. Two particular substrate potentials are considered: theϕ−four and the sine-Gordon (sG). We show that, in the general case where the system exhibits thekink soliton like excitations, the correction factors, due to the lattice discreteness,appearing in the free-energy and in the lattice corrected static kink soliton energy, dependon the temperature through a coupling of the interparticle anharmonicity strength to thetemperature. Similarly, in the purely anharmonic NKG systems, characterized by theabsence of the linear dispersion, where thermodynamic properties are sensitive to kinkcompactons, we find also that the correction factors are temperature dependent. In bothcases, they decrease with increasing temperatures, although the correction factors verifydifferent temperature laws.