Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions

TL;DR

This paper investigates how the decay exponent of repulsive interactions influences long-range stripe order in 2D systems, revealing conditions for order stability and phase transition types.

Contribution

It derives an effective Hamiltonian for stripe systems with variable decay and maps it to an XY model, clarifying the conditions for long-range order and phase transitions.

Findings

Long-range order exists for decay exponent α<2.

No long-range order for α≥2, but a KT transition occurs.

Simulation results support theoretical predictions.

Abstract

We study two dimensional stripe forming systems with competing repulsive interactions decaying as $r^{-\alpha}$. We derive an effective Hamiltonian with a short range part and a generalized dipolar interaction which depends on the exponent $\alpha$. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for $\alpha <2$ long range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When $\alpha \geq 2$ no long-range order is possible, but a phase transition in the KT universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids ($\alpha=1$) and dipolar magnetic films ($\alpha=3$). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.