Canonical Criterion for Third-Order Transitions
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914380859310080 |
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| author | Wang, Fangfang Liu, Wei Qi, Kai Cui, Zidong Tang, Ying Di, Zengru |
| author_facet | Wang, Fangfang Liu, Wei Qi, Kai Cui, Zidong Tang, Ying Di, Zengru |
| contents | Microcanonical inflection-point analysis (MIPA) identifies third-order transitions from derivatives of the microcanonical entropy, but whether such transitions admit a direct canonical formulation has remained unclear. Here we establish a fluctuation-based canonical framework for third-order transitions through a cumulant-ratio criterion whose signed extrema define their canonical counterparts and, in the single-saddle regime, are asymptotically linked to microcanonical classification. Because the criterion depends only on energy cumulants, it avoids explicit density-of-states reconstruction and remains operational in nonequilibrium steady states. Physically, it reveals dependent and independent third-order transitions as fluctuation reorganizations around low-order transitions, namely disordered-side precursors and ordered-side restructuring. Benchmarks on Onsager's two-dimensional Ising solution, finite size Potts models, and a driven nonreciprocal Ising model show that the framework is theoretically grounded and broadly applicable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09124 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Canonical Criterion for Third-Order Transitions Wang, Fangfang Liu, Wei Qi, Kai Cui, Zidong Tang, Ying Di, Zengru Statistical Mechanics Mathematical Physics Microcanonical inflection-point analysis (MIPA) identifies third-order transitions from derivatives of the microcanonical entropy, but whether such transitions admit a direct canonical formulation has remained unclear. Here we establish a fluctuation-based canonical framework for third-order transitions through a cumulant-ratio criterion whose signed extrema define their canonical counterparts and, in the single-saddle regime, are asymptotically linked to microcanonical classification. Because the criterion depends only on energy cumulants, it avoids explicit density-of-states reconstruction and remains operational in nonequilibrium steady states. Physically, it reveals dependent and independent third-order transitions as fluctuation reorganizations around low-order transitions, namely disordered-side precursors and ordered-side restructuring. Benchmarks on Onsager's two-dimensional Ising solution, finite size Potts models, and a driven nonreciprocal Ising model show that the framework is theoretically grounded and broadly applicable. |
| title | Canonical Criterion for Third-Order Transitions |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2603.09124 |