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 10hbox { 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.
Highlights
On the other hand, a comprehension of finite size properties is very important for situations where the deconfinement transition occurs over a finite volume as in relativistic heavy ion collisions and neutron stars
We work at zero chemical potential to compare our numerical results for the bulk with those from lattice Quantum Chromodynamics (QCD) for (2+1)-flavors using the highly improved staggered quark action extrapolated to the continuum limit [48]
We will focus on the order parameters for both chiral and deconfinement transitions showing that, as the temperature is increased at zero baryon chemical potential, the Polyakov loop NJL (PNJL) model presents a smooth crossover transition at T ∼ 150−200 MeV depending on the size
Summary
A comprehension of finite size properties is very important for situations where the deconfinement transition occurs over a finite volume as in relativistic heavy ion collisions and neutron stars. Different thermodynamic quantities calculated within our effective model in the bulk (including three different Polyakov loop potentials) are compared to the corresponding lattice QCD results. This is necessary as a starting point to check the validity of our model. We study the relevance of finite size effects on many properties of strongly interacting matter and analyze how they deviate from the bulk case.
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