Modulated phases of a 1D sharp interface model in a magnetic field

TL;DR

This paper proves that in a one-dimensional continuum magnetic model with competing interactions, the ground states are always simple periodic patterns, regardless of the total magnetization, clarifying the structure of such frustrated systems.

Contribution

It rigorously establishes that the ground states of a 1D continuum model with short-range ferromagnetic and long-range antiferromagnetic interactions are always simple periodic, regardless of magnetization.

Findings

Ground states are simple periodic for all magnetizations.

The result applies to a broad class of models with competing interactions.

It confirms assumptions previously made in condensed matter physics studies.

Abstract

We investigate the ground states of 1D continuum models having short-range ferromagnetic type interactions and a wide class of competing longer-range antiferromagnetic type interactions. The model is defined in terms of an energy functional, which can be thought of as the Hamiltonian of a coarse-grained microscopic system or as a mesoscopic free energy functional describing various materials. We prove that the ground state is simple periodic whatever the prescribed total magnetization might be. Previous studies of this model of frustrated systems assumed this simple periodicity but, as in many examples in condensed matter physics, it is neither obvious nor always true that ground states do not have a more complicated, or even chaotic structure.