Coarse grained models of stripe forming systems: phase diagrams, anomalies and scaling hypothesis

TL;DR

This study investigates two coarse-grained models of stripe forming systems, analyzing their phase diagrams, anomalies, and a scaling hypothesis, revealing universal behaviors and model-specific differences through mean field and fluctuation analyses.

Contribution

The paper introduces two models capturing universal stripe formation features and compares their phase diagrams, fluctuation effects, and scaling behavior, highlighting differences and validating a scaling hypothesis.

Findings

Phase diagrams differ due to k dependence of fluctuation spectrum.

Fluctuations significantly alter mean field predictions.

Scaling hypothesis is validated for both models.

Abstract

Two coarse-grained models which capture some universal characteristics of stripe forming systems are stud- ied. At high temperatures, the structure factors of both models attain their maxima on a circle in reciprocal space, as a consequence of generic isotropic competing interactions. Although this is known to lead to some universal properties, we show that the phase diagrams have important differences, which are a consequence of the particular k dependence of the fluctuation spectrum in each model. The phase diagrams are computed in a mean field approximation and also after inclusion of small fluctuations, which are shown to modify drastically the mean field behavior. Observables like the modulation length and magnetization profiles are computed for the whole temperature range accessible to both models and some important differences in behavior are observed. A stripe compression modulus is computed, showing an anomalous behavior with temperature as recently reported in related models. Also, a recently proposed scaling hypothesis for modulated systems is tested and found to be valid for both models studied.