Phase transitions and finite-size effects in integrable virial statistical models

Fuente: arXiv
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Main Authors: An, Xin, Giglio, Francesco, Landolfi, Giulio
Format: Preprint
Published: 2025
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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
id 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