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arXiv 2010.03310hep-phhep-th
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手征相变的涨落和热力学几何

Fluctuations and thermodynamic geometry of the chiral phase transition

Paolo Castorina, Daniele Lanteri, Marco Ruggieri

摘要:

本文研究了在有限温度和有限化学势下,在增加介子涨落的夸克-介子模型中,手征相变附近的热力学曲率$R$。我们研究了平均场热力学中的π介子和$σ$ -介子的涨落对平均场热力学的影响以及它们如何影响交叉点附近的$R$。我们发现,对于小的化学势的波动增强的幅度$R$,而它们并不影响实质上的热力学几何的临界端点附近。此外,在协议与以前的研究中,我们发现,$R$的变化标志的伪临界区,这表明在介观水平的相互作用的性质的变化,从统计排斥吸引。最后,我们发现,在临界端点周围的临界区域中,$|R|$与相关体积成比例,$|R| =K\;ξ^3$与$K = O(1)$成比例,正如从超标度中所预期的那样;远离临界端点,$|R|$与相关体积之间的对应性不如我们在大$μ$下发现的那么好,这并不奇怪,因为在小$μ$下,手性交叉相当平滑;然而,我们发现$R$形成了一个特征峰结构,这表明它仍然能够捕获冷凝物的假临界行为。

英文摘要:

We study the thermodynamic curvature, $R$, around the chiral phase transition at finite temperature and chemical potential, within the quark-meson model augmented with meson fluctuations. We study the effect of the fluctuations, pions and $σ$-meson, on the top of the mean field thermodynamics and how these affect $R$ around the crossover. We find that for small chemical potential the fluctuations enhance the magnitude of $R$, while they do not affect substantially the thermodynamic geometry in the proximity of the critical endpoint. Moreover, in agreement with previous studies we find that $R$ changes sign in the pseudocritical region, suggesting a change of the nature of interactions at the mesoscopic level from statistically repulsive to attractive. Finally, we find that in the critical region around the critical endpoint $|R|$ scales with the correlation volume, $|R| =K\;ξ^3$, with $K = O(1)$, as expected from hyperscaling; far from the critical endpoint the correspondence between $|R|$ and the correlation volume is not as good as the one we have found at large $μ$, which is not surprising because at small $μ$ the chiral crossover is quite smooth; nevertheless, we have found that $R$ develops a characteristic peak structure, suggesting that it is still capable to capture the pseudocritical behavior of the condensate.

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