Two-Phase Structures as Singular Limit of a one-dimensional Discrete Model

Abstract

A one-dimensional energy functional that models the elastic free energy of a monatomic chain of atoms occupying a bounded real domain is discussed and the Γ-limit of this functional when the number of particles becomes infinite is derived. The particular ansatz allows for the first time the presence of two coexisting phases in the singular limit and thus can be used as a prototype towards modeling three dimensional cases of physical relevance.