Statistical mechanics of the continuum and discrete Phi4system with long-range interaction potential: the soliton dilute-gas phenomenology

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Abstract
The soliton dilute-gas phenomenology is used to study the statistical mechanics of the Phi 4 system with long-range interaction potential. Both the continuum and the discrete phonon excitations with their corresponding dispersion relations and non-linear excitations (walls or kinks) are investigated. In the continuum model, the authors show that the kink free energy and density decrease when the range of interaction increases. In the discrete model where the kink width is small, as a result of the collective coordinate method associated with Dirac's constrained Hamiltonian dynamics, the mass and the potential energy of kink vary periodically with the kink position in the lattice. This leads to a correction of the statistical results obtained in the continuum model.