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MiS Preprint

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.

MSC Codes:
49J45, 49N45, 82B24
phrase transitions, singular perturbations, gamma-convergence, nonlocal integral functionals

Related publications

1998 Repository Open Access
Giovanni Alberti and Giovanni Bellettini

A non-local anisotropic model for phase transitions : asymptotic behavior of rescaled energies

In: European journal of applied mathematics, 9 (1998) 3, pp. 261-284