Criticality and Universality of Generalized Kuramoto Model
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908355967057920 |
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| author | Qiu, Zhongpu Wu, Tianyi Fang, Sheng Meng, Jun Fan, Jingfang |
| author_facet | Qiu, Zhongpu Wu, Tianyi Fang, Sheng Meng, Jun Fan, Jingfang |
| contents | We explore synchronization transitions in even-$D$-dimensional generalized Kuramoto oscillators on both complete graphs and $d$-dimensional lattices. In the globally coupled system, analytical expansions of the self-consistency equations, incorporating finite-size corrections, reveal universal critical exponents $β= 1/2$ and $\barν = 5/2$ for all even $D$, indicating an unconventional upper critical dimension $d_u = 5$. Extensive numerical simulations across multiple $D$ confirm these theoretical predictions. For locally coupled systems, we develop a framework based on spin-wave theory and fluctuation-resolved functional network diagnostics, which captures criticality in entrainment transition. A modified Edwards-Anderson order parameter further validates the predicted exponents. This combined theoretical and numerical study uncovers a family of universality classes characterized by $D$-independent but $d$-dependent criticality, offering a unified perspective on symmetry and dimensionality in nonequilibrium synchronization phenomena. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Criticality and Universality of Generalized Kuramoto Model Qiu, Zhongpu Wu, Tianyi Fang, Sheng Meng, Jun Fan, Jingfang Statistical Mechanics We explore synchronization transitions in even-$D$-dimensional generalized Kuramoto oscillators on both complete graphs and $d$-dimensional lattices. In the globally coupled system, analytical expansions of the self-consistency equations, incorporating finite-size corrections, reveal universal critical exponents $β= 1/2$ and $\barν = 5/2$ for all even $D$, indicating an unconventional upper critical dimension $d_u = 5$. Extensive numerical simulations across multiple $D$ confirm these theoretical predictions. For locally coupled systems, we develop a framework based on spin-wave theory and fluctuation-resolved functional network diagnostics, which captures criticality in entrainment transition. A modified Edwards-Anderson order parameter further validates the predicted exponents. This combined theoretical and numerical study uncovers a family of universality classes characterized by $D$-independent but $d$-dependent criticality, offering a unified perspective on symmetry and dimensionality in nonequilibrium synchronization phenomena. |
| title | Criticality and Universality of Generalized Kuramoto Model |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2505.05760 |