https://doi.org/10.1140/epjb/s10051-025-01040-y
Research - Condensed Matter
Stripe order in quasicrystals
Instituto de Física, Universidade de São Paulo, 05315-970, São Paulo, SP, Brazil
a
rmarques@if.usp.br
b
eandrade@if.usp.br
Received:
24
June
2025
Accepted:
2
September
2025
Published online:
14
September
2025
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 
-
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 , a Néel phase appears, whereas a stripe phase is stable for dominant antiferromagnetic , 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.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
