Finite volume effects on the chiral phase transition from Dyson-Schwinger equations of QCD

TL;DR

This study uses Dyson-Schwinger equations to analyze how finite volume influences the chiral phase transition and the position of the pseudo-critical end point in QCD, revealing volume-dependent shifts in critical temperatures and phase transition nature.

Contribution

It provides a detailed analysis of finite volume effects on the chiral phase transition and pseudo-critical end point within Dyson-Schwinger equations, highlighting volume-dependent shifts and potential crossover behavior.

Findings

Smaller volumes decrease quark condensate and critical temperature in the chiral limit.

Pseudo-critical temperature decreases with smaller volume, while chemical potential increases.

Very small systems may undergo a crossover transition with no pseudo-critical end point.

Abstract

Within the framework of Dyson-Schwinger equations of QCD, we study the finite volume effects on the chiral phase transition, especially the influence on the position of the possible pseudo-critical end point (pCEP). The results show that in the chiral limit case (the current quark mass $m=0$), the absolute value of quark condensate decreases for smaller volumes, and more interestingly, so does the pseudo-critical temperature $T_c(\mu=0)$, which is in agreement with the Polyakov Nambu--Jona-Lasinio model result and opposite to the Polyakov linear sigma model prediction. These conclusions hold for $m>0$ case in our calculations. Moreover, the results of pCEP as a function of different volumes show that $T$ of pCEP also decreases for smaller volumes, but $\mu$ of pCEP will increase, which are qualitatively more close to Polyakov linear sigma model results. For our model setup, results for systems with a size larger than (5 fm)$^3$ closely approximate those from infinite volume, but if the volume is smaller, the corrections are non-negligible, even significantly affect signatures of the results from an infinite system. There also exists some possibility that, if the system size is too small, the whole phase transition would be crossover, which means no pCEP exists at all. It is no doubt that, finite volume effects deserve further researches.