1. On the surface tension for non local energy functionals
- Author
-
Cristiana Bisceglia and Emanuele Rosatelli
- Subjects
coexistence of phases ,surface tension ,γ- convergence ,Mathematics ,QA1-939 - Abstract
We consider the free energy functional F_ε(m), ε > 0 a scaling parameter, m ∈ L∞(T;[−1, 1]), T the unit torus, which has been derived in a continuum limit from Ising spin systems with Kac interactions, see [8]. In [1] it is proved that F_ε(m) Γ−converges to a perimeter functional P. We study here the free energy functional with an additional term describing the interaction with an external magnetic field h. We suppose that h takes only the two values ±s, s > 0. Calling E the region of the torus where the external field is negative and Fε,s(m; E) the new functional, we then define G_{ε,s}(E) = inf_m F_{ε,s}(m; E). We prove that G_{ε,s}(·) Γ−converges to a perimeter functional which as a function of s converges pointwise as s → 0 to P.
- Published
- 2005