Universality Diagram of Phase Transitions in Long-range Statistical Systems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915738944536576 |
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| author | Xiao, Tianning Fan, Zhijie Deng, Youjin |
| author_facet | Xiao, Tianning Fan, Zhijie Deng, Youjin |
| contents | The percolation, Ising, and O($n$) models constitute fundamental systems in statistical and condensed matter physics. For short-range-interacting cases, the nature of their phase transitions is well established by renormalization-group theory. However, the universality of the transitions in these models remains elusive when algebraically decaying long-range interactions $\sim 1/r^{d+σ}$ are introduced, where $d$ is the dimensionality and $σ$ is the decay exponent. Building upon insights from Lévy flight, i.e., long-range simple random walk, we propose three universality diagrams in the $(d,σ)$ plane for the percolation model, the O($n$) model, and the Fortuin-Kasteleyn Ising model, respectively. The conjectured universality diagrams are consistent with recent high-precision numerical studies and rigorous mathematical results, offering a unified perspective on critical phenomena in systems with long-range interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality Diagram of Phase Transitions in Long-range Statistical Systems Xiao, Tianning Fan, Zhijie Deng, Youjin Statistical Mechanics The percolation, Ising, and O($n$) models constitute fundamental systems in statistical and condensed matter physics. For short-range-interacting cases, the nature of their phase transitions is well established by renormalization-group theory. However, the universality of the transitions in these models remains elusive when algebraically decaying long-range interactions $\sim 1/r^{d+σ}$ are introduced, where $d$ is the dimensionality and $σ$ is the decay exponent. Building upon insights from Lévy flight, i.e., long-range simple random walk, we propose three universality diagrams in the $(d,σ)$ plane for the percolation model, the O($n$) model, and the Fortuin-Kasteleyn Ising model, respectively. The conjectured universality diagrams are consistent with recent high-precision numerical studies and rigorous mathematical results, offering a unified perspective on critical phenomena in systems with long-range interactions. |
| title | Universality Diagram of Phase Transitions in Long-range Statistical Systems |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2512.02948 |