Finite size effects in strongly interacting matter at zero chemical potential from Polyakov loop Nambu-Jona-Lasinio model in the light of lattice data

Abstract

We study finite volume effects within the Polyakov loop Nambu-Jona-Lasinio model for two light and one heavy quarks at vanishing baryon chemical potential and finite temperatures. We include three different Polyakov loop potentials and ensure that the predictions of our effective model in bulk are compatible with lattice QCD results. Finite size effects are taken into account by means of the Multiple Reflection Expansion formalism. We analyze several thermodynamic quantities including the interaction measure, the speed of sound, the surface tension, and the curvature energy and find that they are sensitive to finite volume effects, specially for systems with radii below $\sim 10$ fm and temperatures around the crossover one. For all sizes, the system undergoes a smooth crossover. The chiral critical temperature decreases by around $5 \%$ and the deconfinement temperature by less than a $2 \%$ when the radius goes from infinity to 3 fm. Thus, as the drop's size decreases, both temperatures become closer. The surface tension is dominated by the contribution of strange quarks and the curvature energy by $u$ and $d$ quarks. At large temperatures both quantities grow proportionally to $T^{3/2}$ but saturate to a constant value at low $T$.