Modulation and correlations lengths in systems with competing interactions

TL;DR

This paper investigates how competing long and short-range interactions influence correlation and modulation lengths in systems like Ising ferromagnets, revealing conserved lengths and temperature-dependent behaviors.

Contribution

It provides analytical calculations of ground state stripe widths, crossover temperature behaviors, and modulation length changes in systems with competing interactions, including dipolar effects.

Findings

Crossover temperature approaches the unfrustrated critical temperature.

Total number of correlation and modulation lengths remains conserved except at special points.

Exact dipolar correlations differ significantly from simplified scalar product models.

Abstract

We examine correlation functions in the presence of competing long and short ranged interactions to find multiple correlation and modulation lengths. We calculate the ground state stripe width of an Ising ferromagnet, frustrated by an arbitrary long range interaction. In large $n$ systems, we demonstrate that for a short range system frustrated by a general competing long range interaction, the crossover temperature $T^*$ veers towards the critical temperature of the unfrustrated short range system (i.e., that in which the frustrating long range interaction is removed). We also show that apart from certain special crossover points, the total number of correlation and modulation lengths remains conserved. We derive an expression for the change in modulation length with temperature for a general system near the ground state with a ferromagnetic interaction and an opposing long range interaction. We illustrate that the correlation functions associated with the exact dipolar interactions differ substantially from those in which a scalar product form between the dipoles is assumed.