标题： 量子色动力学相变附近的热力学几何的函数重整化群研究 显示英文标题

标题： Functional Renormalization Group Study of Thermodynamic Geometry Around the Phase Transition of Quantum Chromodynamic

摘要： 我们研究有限温度下夸克-介子模型的热力学几何，$T$，以及夸克数化学势，$\mu$。 我们通过引入涨落扩展了之前的工作，利用功能重整化群方法。 我们利用最近的发展将流动方程重新表述为对流-扩散方程的形式。 我们采用有效平均作用的局部势近似。 我们关注热力学曲率，$R$，在$(\mu,T)$平面中接近手征转变区域，直至相图中的临界点。 我们发现，引入涨落使得$R$在手征转变附近表现出更平滑的行为。 此外，对于小的$\mu$，$R$保持负值，表明玻色涨落降低了系统完全克服夸克费米统计排斥的能力。 我们通过分析一个人为降低介子质量的系统，更详细地研究了小 $\mu$ 区域，从而接近实际为二阶相变的手征极限。 另一方面，当 $\mu$ 增加并接近临界点时，我们发现 $R$ 被增强，并发生符号变化，这与均场研究结果一致。 因此，我们完全支持这样的观点，即 $R$ 对于平滑相变和相变敏感，并提供了关于相变时系统有效行为的信息。 显示英文摘要

摘要： We investigate the thermodynamic geometry of the quark-meson model at finite temperature, $T$, and quark number chemical potential, $\mu$. We extend previous works by the inclusion of fluctuations exploiting the functional renormalization group approach. We use recent developments to recast the flow equation into the form of an advection-diffusion equation. We adopt the local potential approximation for the effective average action. We focus on the thermodynamic curvature, $R$, in the $(\mu,T)$ plane, in proximity of the chiral crossover, up to the critical point of the phase diagram. We find that the inclusion of fluctuations results in a smoother behavior of $R$ near the chiral crossover. Moreover, for small $\mu$, $R$ remains negative, signaling the fact that bosonic fluctuations reduce the capability of the system to completely overcome the fermionic statistical repulsion of the quarks. We investigate in more detail the small $\mu$ region by analyzing a system in which we artificially lower the pion mass, thus approaching the chiral limit in which the crossover is actually a second order phase transition. On the other hand, as $\mu$ is increased and the critical point is approached, we find that $R$ is enhanced and a sign change occurs, in agreement with mean field studies. Hence, we completely support the picture that $R$ is sensitive to a crossover and a phase transition, and provides information about the effective behavior of the system at the phase transition.