Periodic striped states in Ising models with dipolar interactions

TL;DR

This paper investigates the ground states of 2D Ising models with dipolar interactions, proving that for large nearest neighbor coupling, the states are periodic and striped, within a specific class of configurations.

Contribution

It provides a new proof supporting the conjecture that large coupling leads to striped ground states, focusing on a restricted class of configurations.

Findings

Ground states are periodic and striped for large J

Constructed minimizers within a class of straight-line domain walls

Supports the conjecture on the nature of ground states in dipolar Ising models

Abstract

We review the problem of determining the ground states of 2D Ising models with nearest neighbor ferromagnetic and dipolar interactions, and prove a new result supporting the conjecture that, if the nearest neighbor coupling $J$ is sufficiently large, the ground states are periodic and `striped'. More precisely, we prove a restricted version of the conjecture, by constructing the minimizers within the variational class of states whose domain walls are arbitrary collections of horizontal and/or vertical straight lines.