Stripe order in quasicrystals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914046707499008 |
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| author | Teixeira, Rafael M. P. Andrade, Eric C. |
| author_facet | Teixeira, Rafael M. P. Andrade, Eric C. |
| contents | 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 Néel 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stripe order in quasicrystals Teixeira, Rafael M. P. Andrade, Eric C. Strongly Correlated Electrons Statistical Mechanics 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 Néel 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. |
| title | Stripe order in quasicrystals |
| topic | Strongly Correlated Electrons Statistical Mechanics |
| url | https://arxiv.org/abs/2506.11230 |