Inserted: 13 oct 2016
Last Updated: 12 mar 2018
Journal: Ann.Mat.Pura Appl
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