We investigate the thermodynamic geometry of the quark-meson model at finitetemperature, $T$, and quark number chemical potential, $\mu$. We extendprevious works by the inclusion of fluctuations exploiting the functionalrenormalization group approach. We use recent developments to recast the flowequation into the form of an advection-diffusion equation. We adopt the localpotential approximation for the effective average action. We focus on thethermodynamic curvature, $R$, in the $(\mu,T)$ plane, in proximity of thechiral crossover, up to the critical point of the phase diagram. We find thatthe inclusion of fluctuations results in a smoother behavior of $R$ near thechiral crossover. Moreover, for small $\mu$, $R$ remains negative, signalingthe fact that bosonic fluctuations reduce the capability of the system tocompletely overcome the fermionic statistical repulsion of the quarks. Weinvestigate in more detail the small $\mu$ region by analyzing a system inwhich we artificially lower the pion mass, thus approaching the chiral limit inwhich the crossover is actually a second order phase transition. On the otherhand, as $\mu$ is increased and the critical point is approached, we find that$R$ is enhanced and a sign change occurs, in agreement with mean field studies.Hence, we completely support the picture that $R$ is sensitive to a crossoverand a phase transition, and provides information about the effective behaviorof the system at the phase transition.
Functional Renormalization Group Study of Thermodynamic Geometry Around the Phase Transition of Quantum Chromodynamic
Fabrizio Murgana
;Vincenzo Greco;Marco Ruggieri;
2024-01-01
Abstract
We investigate the thermodynamic geometry of the quark-meson model at finitetemperature, $T$, and quark number chemical potential, $\mu$. We extendprevious works by the inclusion of fluctuations exploiting the functionalrenormalization group approach. We use recent developments to recast the flowequation into the form of an advection-diffusion equation. We adopt the localpotential approximation for the effective average action. We focus on thethermodynamic curvature, $R$, in the $(\mu,T)$ plane, in proximity of thechiral crossover, up to the critical point of the phase diagram. We find thatthe inclusion of fluctuations results in a smoother behavior of $R$ near thechiral crossover. Moreover, for small $\mu$, $R$ remains negative, signalingthe fact that bosonic fluctuations reduce the capability of the system tocompletely overcome the fermionic statistical repulsion of the quarks. Weinvestigate in more detail the small $\mu$ region by analyzing a system inwhich we artificially lower the pion mass, thus approaching the chiral limit inwhich the crossover is actually a second order phase transition. On the otherhand, as $\mu$ is increased and the critical point is approached, we find that$R$ is enhanced and a sign change occurs, in agreement with mean field studies.Hence, we completely support the picture that $R$ is sensitive to a crossoverand a phase transition, and provides information about the effective behaviorof the system at the phase transition.File | Dimensione | Formato | |
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