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 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 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| = Kξ 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.

Finite Size Effects on the Chiral Phase Transition of Quantum Chromodynamics

“…There are several ways to continue the work presented here. A straightforward extension of the work is the inclusion of meson fluctuations on the same line of [31]. It would be interesting to include the possibility of inhomogeneous condensates [32][33][34][35][36][37][38][39][40][41].…”

“…The inclusion of the Polyakov loop to take trace of confinementdeconfinement phase transition via a collective field would also be possible [42][43][44]. Finally, it is of a certain interest to analyze the thermodynamic geometry [31,[45][46][47][48][49][50][51][52][53][54] of the effective models of chiral symmetry breaking with finite size. We plan to report on these topics in the near future.…”

“…To do this, firstly we have to compute the in-medium masse of the σ−meson. Computing this within the quark-meson model is a well established procedure, see for example [31] and references therein, and is straightforward when two-loop contributions are neglected and the Hatree approximation is used to compute the effective 2-particle-irreducible potential. Within these approximations we have M 2 σ = ∂ 2 Ω/∂σ 2 , where the second derivative is understood at the global minimum of Ω.…”