The XY model with vision cone: non-reciprocal vs. reciprocal interactions

We study the behavior of the classical XY model on a two-dimensional square lattice, with interactions occurring within a vision cone of each spin. Via Monte Carlo simulations, we explore one non-reciprocal and two reciprocal implementations of these interactions. The corresponding energy involves c...

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Bibliographic Details
Published inJournal of statistical mechanics Vol. 2025; no. 5; pp. 53205 - 53245
Main Authors Bandini, Gabriele, Venturelli, Davide, Loos, Sarah A M, Jelic, Asja, Gambassi, Andrea
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.05.2025
Subjects
active matter
classical Monte Carlo simulations
classical phase transitions
phase diagrams
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Summary:We study the behavior of the classical XY model on a two-dimensional square lattice, with interactions occurring within a vision cone of each spin. Via Monte Carlo simulations, we explore one non-reciprocal and two reciprocal implementations of these interactions. The corresponding energy involves couplings that depend non-trivially on the system’s configuration, leading to both long-range and quasi-long-range ordered phases at low temperatures. Our results demonstrate that non-reciprocity is not essential for achieving long-range order at low temperatures. Using symmetry arguments, we provide a theoretical framework to explain these findings, and additionally we uncover an unexpected order-by-disorder transition.
Bibliography:JSTAT_020P_0125
ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/adc243