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arXiv · 2506.11230

Stripe order in quasicrystals

Rafael M. P. Teixeira·Eric C. Andrade
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Abstract

We explore the emergence of magnetic order in geometrically frustrated quasiperiodic systems, focusing on the interplay between local tile symmetry and frustration-induced constraints. In particular, we study the $J_1$-$J_2$ Ising model on the two-dimensional Ammann--Beenker quasicrystal. Through large-scale Monte Carlo simulations and general arguments, we map the phase diagram of the model. For small $J_2$, a N\'eel phase appears, whereas a stripe phase is stable for dominant antiferromagnetic $J_2$, despite the system's lack of periodicity. Although long-range stripe order emerges below a critical temperature, unlike in random systems, it is softened by the nucleation of competing stripe domains pinned at specific quasiperiodic sites. This behavior reveals a unique mechanism of symmetry breaking in quasiperiodic lattices, where geometric frustration and local environment effects compete to determine the magnetic ground state. Our results show how long-range order adapts to non-periodic structures, with implications for understanding nematic phases and other broken-symmetry states in quasicrystals.

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Rafael M. P. Teixeira, Eric C. Andrade. 2025-06-12. Stripe order in quasicrystals. https://doi.org/10.1140/epjb%2Fs10051-025-01040-y

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