Synchronization and phase transition of two-dimensional self-rotating clock models
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912862675402752 |
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| author | Wu, Xin Yang, Mingcheng |
| author_facet | Wu, Xin Yang, Mingcheng |
| contents | We explore possible synchronization in two-dimensional (2D) locally coupled discrete-state oscillators under thermal fluctuations, using the self-rotating $q$-state clock model as a prototype. Large-scale Monte Carlo simulations reveal that for $q \ge q_c$ (with $q_c = 5$), the system undergoes two-step Berezinskii-Kosterlitz-Thouless (BKT) transitions: first from a disordered phase to a critical synchronized phase, and then to a spatiotemporal pattern phase. The latter includes oscillatory droplet states that survive in finite systems and a thermodynamically stable spiral wave state. Notably, the synchronized phase features algebraically decaying spatial correlations, alongside divergent coherence time, thus realizing a continuous time crystal; while it vanishes when $q < q_c$. Mean-field theory supports the existence of the synchronized phase, but predicts a lower critical value $q_c^{MF} = 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22840 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Synchronization and phase transition of two-dimensional self-rotating clock models Wu, Xin Yang, Mingcheng Statistical Mechanics Adaptation and Self-Organizing Systems Pattern Formation and Solitons We explore possible synchronization in two-dimensional (2D) locally coupled discrete-state oscillators under thermal fluctuations, using the self-rotating $q$-state clock model as a prototype. Large-scale Monte Carlo simulations reveal that for $q \ge q_c$ (with $q_c = 5$), the system undergoes two-step Berezinskii-Kosterlitz-Thouless (BKT) transitions: first from a disordered phase to a critical synchronized phase, and then to a spatiotemporal pattern phase. The latter includes oscillatory droplet states that survive in finite systems and a thermodynamically stable spiral wave state. Notably, the synchronized phase features algebraically decaying spatial correlations, alongside divergent coherence time, thus realizing a continuous time crystal; while it vanishes when $q < q_c$. Mean-field theory supports the existence of the synchronized phase, but predicts a lower critical value $q_c^{MF} = 4$. |
| title | Synchronization and phase transition of two-dimensional self-rotating clock models |
| topic | Statistical Mechanics Adaptation and Self-Organizing Systems Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2601.22840 |