Calculus of Variations and Geometric Measure Theory

A. Braides - A. Causin - M. Solci

Asymptotic analysis of a ferromagnetic Ising system with "diffuse" interfacial energy

created by braidesa on 13 Oct 2016
modified on 12 Mar 2018


Published Paper

Inserted: 13 oct 2016
Last Updated: 12 mar 2018

Journal: Ann.Mat.Pura Appl
Volume: 197
Number: 2
Pages: 583-604
Year: 2018
Doi: 10.1007/s10231-017-0693-9


We give an example of a one-dimensional scalar spin energy with long-range interactions not satisfying standard decay conditions and which admits a continuum approximation defined for functions $u$ in $BV((0,L),[-1,1])$ taking into account the total variation of $u$. Related minimum problems show boundary and size effects in dependence of $L$.

Keywords: discrete-to-continuum, Ising-type energies, Interfacial energies, Size effects