Fluctuations and thermodynamic geometry of the chiral phase transition

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 s 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 jRj scales with the correlation volume, vertical bar R vertical bar = K xi(3) with K = O(1) as expected from hyperscaling; far from the critical end point the correspondence between vertical bar R vertical bar 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 groove structure, suggesting that it is still capable to capture the pseudocritical behavior of the condensate.