标题： 可积级数统计模型中的相变和有限尺寸效应 显示英文标题

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

摘要： 我们基于内能的体积密度展开式分析流体系统的热力学模型。 我们证明，对于具有$N$个粒子的有限尺寸系统所制定的模型，在任何展开阶数上都是精确可解的，因为物理可观测量（例如体积密度）的期望值由一类非线性C-可积流体类型偏微分方程的解确定。 在$N\to\infty$极限下，相变作为热力学变量空间中的经典冲击波出现。 在临界点附近，我们认为体积密度表现出与粘性输运偏微分方程中的普遍性假设一致的标度行为。 作为应用，我们利用我们的框架研究核物质，并构建一个全局的QCD相图，揭示核液气和强子气体-夸克胶子等离子体相变的临界点。 我们展示了有限尺寸效应如何模糊临界特征，这表明在寻找QCD临界点时需要仔细考虑。 显示英文摘要

摘要： 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 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 matter and construct a global QCD phase diagram revealing critical points for the nuclear liquid-gas and hadron gas-QGP transitions. We demonstrate how finite-size effects smear critical signatures, indicating the importance of thoughtful considerations in the search for the QCD critical point.