Fluctuations and thermodynamic geometry of the chiral phase transition

TL;DR

This study investigates the thermodynamic curvature near the chiral phase transition using the quark-meson model, revealing how fluctuations influence the geometry and indicating a change in interaction nature at the mesoscopic level.

Contribution

It provides a detailed analysis of the thermodynamic curvature and its relation to fluctuations and correlation volume around the chiral phase transition, including near the critical endpoint.

Findings

Fluctuations enhance the magnitude of R at small chemical potential.

R changes sign in the pseudocritical region, indicating a shift in interaction nature.

|R| scales with the correlation volume near the critical endpoint.

Abstract

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 $\sigma$-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, $|R| =K\;\xi^3$, 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 $\mu$, which is not surprising because at small $\mu$ 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.