Phase transitions and finite-size effects in integrable virial statistical models
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| Format: | Preprint |
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2025
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| _version_ | 1866915943878230016 |
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| author | An, Xin Giglio, Francesco Landolfi, Giulio |
| author_facet | An, Xin Giglio, Francesco Landolfi, Giulio |
| contents | We analyze thermodynamic models for fluid systems in equilibrium based on a virial expansion of the internal energy in terms of the volume density. We prove that the models, formulated for finite-size systems with $N$ particles, are exactly solvable to any expansion order, as expectation values of physical observables (e.g., volume density) are determined from solutions to nonlinear C-integrable partial differential equations (PDEs) of hydrodynamic type. In the limit $N\to \infty$, phase transitions emerge as classical shock waves in the space of thermodynamic variables. Near critical points, we argue that the volume density exhibits a scaling behavior consistent with the Universality Conjecture in viscous transport PDEs. As an application, we employ our framework to nuclear and quark matter, constructing a global quantum chromodynamics (QCD) phase diagram that reveals critical points for the nuclear liquid-gas transition and the hadron gas-quark-gluon plasma transition. We demonstrate how finite-size effects smear critical signatures, implying their potential impact on the search for the QCD critical point. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_15719 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase transitions and finite-size effects in integrable virial statistical models An, Xin Giglio, Francesco Landolfi, Giulio Statistical Mechanics High Energy Physics - Theory Exactly Solvable and Integrable Systems Nuclear Theory We analyze thermodynamic models for fluid systems in equilibrium based on a virial expansion of the internal energy in terms of the volume density. We prove that the models, formulated for finite-size systems with $N$ particles, are exactly solvable to any expansion order, as expectation values of physical observables (e.g., volume density) are determined from solutions to nonlinear C-integrable partial differential equations (PDEs) of hydrodynamic type. In the limit $N\to \infty$, phase transitions emerge as classical shock waves in the space of thermodynamic variables. Near critical points, we argue that the volume density exhibits a scaling behavior consistent with the Universality Conjecture in viscous transport PDEs. As an application, we employ our framework to nuclear and quark matter, constructing a global quantum chromodynamics (QCD) phase diagram that reveals critical points for the nuclear liquid-gas transition and the hadron gas-quark-gluon plasma transition. We demonstrate how finite-size effects smear critical signatures, implying their potential impact on the search for the QCD critical point. |
| title | Phase transitions and finite-size effects in integrable virial statistical models |
| topic | Statistical Mechanics High Energy Physics - Theory Exactly Solvable and Integrable Systems Nuclear Theory |
| url | https://arxiv.org/abs/2503.15719 |