Asymptotic analysis of a ferromagnetic lattice spin system with diffuse interfacial energy

TL;DR

This paper investigates a one-dimensional ferromagnetic spin system with long-range interactions, demonstrating a continuum approximation involving total variation and revealing boundary and size effects based on system length.

Contribution

It introduces a continuum approximation for a non-standard long-range interacting spin system, highlighting boundary and size effects in the energy minimization problem.

Findings

Continuum approximation involving total variation for the spin system.

Boundary and size effects depend on the system length L.

Example of a non-standard decay condition in long-range interactions.

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.