# Thermodynamic Geometry of the Quark-Meson Model

## TL;DR

This paper investigates the thermodynamic geometry of the Quark-Meson model, revealing how the curvature behaves near the chiral crossover and critical endpoint, indicating growing correlations and phase transition signatures.

## Contribution

It provides a detailed analysis of the thermodynamic curvature and fluctuations in the Quark-Meson model, highlighting behavior near the critical endpoint.

## Key findings

- Curvature $R$ changes sign and peaks near the crossover.
- Peak height of $R$ diverges at the critical endpoint.
- Fluctuations of energy and baryon number grow near the critical point.

## Abstract

We study the thermodynamic geometry of the Quark-Meson model, focusing on the curvature, $R$, around the chiral crossover at finite temperature and baryon chemical potential. We find a peculiar behavior of $R$ in the crossover region, in which the sign changes and a local maximum develops; in particular, the height of the peak of $R$ in the crossover region becomes large in proximity of the critical endpoint and diverges at the critical endpoint. The appearance of a pronounced peak of $R$ close to the critical endpoint supports the idea that $R$ grows with the correlation volume around the phase transition. We also analyze the mixed fluctuations of energy and baryon number, $\langle\Delta U\Delta N\rangle$, which grow up substantially in proximity of the critical endpoint: in the language of thermodynamic geometry these fluctuations are responsible for the vanishing of the determinant of the metric, which results in thermodynamic instability and are thus related to the appearance of the second order phase transition at the critical endpoint.