Fluctuations and thermodynamic geometry of the chiral phase transition

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 $\ensuremath{\sigma}$ 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 proximity of the critical end point. 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 end point $|R|$ scales with the correlation volume, $|R|=K{\ensuremath{\xi}}^{3}$ with $K=O(1)$, as expected from hyperscaling; far from the critical end point the correspondence between $|R|$ and the correlation volume is not as good as the one we have found at large $\ensuremath{\mu}$, which is not surprising because at small $\ensuremath{\mu}$ the chiral crossover is quite smooth; nevertheless, we have found that $R$ develops a characteristic groove structure, suggesting that it is still capable to capture the pseudocritical behavior of the condensate.

Topics & Concepts