Self-induced glassiness and pattern formation in spin systems subject to long-range interactions

TL;DR

This paper investigates how long-range interactions and anisotropy influence glass formation and pattern emergence in 2D and 3D spin systems, revealing conditions for stable glassy phases and pattern modulation.

Contribution

It introduces a mean-field framework to analyze glassiness and pattern formation in spin systems with competing interactions and anisotropy, highlighting differences between two and three dimensions.

Findings

Glass phase exists in 3D below a critical anisotropy.

In 3D, strong anisotropy leads to striped phases.

In 2D, glassy phases are always present regardless of anisotropy.

Abstract

We study the glass formation in two- and three-dimensional Ising and Heisenberg spin systems subject to competing interactions and uniaxial anisotropy with a mean-field approach. In three dimensions, for sufficiently strong anisotropy the systems always modulates in a striped phase. Below a critical strength of the anisotropy, a glassy phase exists in a finite range of temperature, and it becomes more stable as the system becomes more isotropic. In two dimension the criticality is always avoided and the glassy phase always exists.