Supercritical-subcritical correspondence, asymmetric effects and antisymmetric corrections near a critical point
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917135197929472 |
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| author | Li, Xinyang Jin, Yuliang |
| author_facet | Li, Xinyang Jin, Yuliang |
| contents | The second-order phase transitions in the Ising model and liquid-gas systems share a universality class and critical exponents, despite the absence of $Z_2$ symmetry in the liquid-gas Hamiltonian. This discrepancy highlights a central puzzle in critical phenomena: what is the influence of asymmetry on scaling laws? For over a century, this question has been explored through examining violations of the empirical ``rectilinear diameter law'' for the subcritical coexistence curve, where asymmetry could generate singular corrections. Here, we extend this investigation to the supercritical regime. We propose a supercritical-subcritical correspondence, drawing a formal analogy between the subcritical coexistence curve and recently defined supercritical boundary lines ($L^\pm$ lines). Our theory predicts that the linear mixing of physical fields - a hallmark of asymmetric systems - produces universal scaling corrections, with antisymmetric coefficients, in these supercritical loci. We verify these predictions using liquid-gas data from the NIST database and a model liquid-liquid transition. Furthermore, we demonstrate that the same asymmetric scaling framework governs the behavior of higher-order cumulants in the order parameter distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08553 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Supercritical-subcritical correspondence, asymmetric effects and antisymmetric corrections near a critical point Li, Xinyang Jin, Yuliang Statistical Mechanics The second-order phase transitions in the Ising model and liquid-gas systems share a universality class and critical exponents, despite the absence of $Z_2$ symmetry in the liquid-gas Hamiltonian. This discrepancy highlights a central puzzle in critical phenomena: what is the influence of asymmetry on scaling laws? For over a century, this question has been explored through examining violations of the empirical ``rectilinear diameter law'' for the subcritical coexistence curve, where asymmetry could generate singular corrections. Here, we extend this investigation to the supercritical regime. We propose a supercritical-subcritical correspondence, drawing a formal analogy between the subcritical coexistence curve and recently defined supercritical boundary lines ($L^\pm$ lines). Our theory predicts that the linear mixing of physical fields - a hallmark of asymmetric systems - produces universal scaling corrections, with antisymmetric coefficients, in these supercritical loci. We verify these predictions using liquid-gas data from the NIST database and a model liquid-liquid transition. Furthermore, we demonstrate that the same asymmetric scaling framework governs the behavior of higher-order cumulants in the order parameter distribution. |
| title | Supercritical-subcritical correspondence, asymmetric effects and antisymmetric corrections near a critical point |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2512.08553 |