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

Abstract:

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

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