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A nonlocal anisotropic model for phase transitions. Part II: Asymptotic behaviour of rescaled energies
Giovanni Alberti and Giovanni Bellettini
In this paper we study the asymptotic behaviour in the thermodynamic limit of a non local model for phase separation. More precisely we consider the free energy obtained by replacing the usual gradient term in the Cahn-Hilliard model with an interaction energy associated to a positive non-isotropic interaction potential, and then we show that the limit in the sense of Gamma-convergence of suitable rescalings of this energy leads to the classical (non-isotropic) model for surface tension. These functionals appear in statistical mechanics as free energies of Ising systems with Kac potential.