Stripe order in quasicrystals

Rafael M. P. Teixeira () and Eric C. Andrade ()
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Rafael M. P. Teixeira: Universidade de São Paulo
Eric C. Andrade: Universidade de São Paulo

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 9, 1-9

Abstract: 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 1 - $$J_2$$ 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 $$J_2$$ J 2 , a Néel phase appears, whereas a stripe phase is stable for dominant antiferromagnetic $$J_2$$ 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. Graphic abstract

Date: 2025
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DOI: 10.1140/epjb/s10051-025-01040-y

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