Finite Size Effects on the Chiral Phase Transition of Quantum Chromodynamics

Abstract

We study the effect of periodic boundary conditions on chiral symmetry breaking and its restoration in Quantum Chromodynamics. As an effective model of the effective potential for the quark condensate, we use the quark-meson model, while the theory is quantized in a cubic box of size L. After specifying a renormalization prescription for the vacuum quark loop, we study the condensate at finite temperature, T , and quark chemical potential, µ. We find that lowering L leads to a catalysis of chiral symmetry breaking. The excitation of the zero mode leads to a jump in the condensate at low temperature and high density, that we suggest to interpret as a gas-liquid phase transition that takes place between the chiral symmetry broken phase (hadron gas) and chiral symmetry restored phase (quark matter). We characterize this intermediate phase in terms of the increase of the baryon density, and of the correlation length of the fluctuations of the order parameter: for small enough L the correlation domains occupy a substantial portion of the volume of the system, and the fluctuations are comparable to those in the critical region. For these reasons, we dub this phase as the subcritical liquid. The qualitative picture that we draw is in agreement with previous studies based on similar effective models. We also clarify the discrepancy on the behavior of the critical temperature versus L found in different models.

Hyper-order baryon number fluctuations at finite temperature and density

“…[94][95][96], finite volume effects on the location of the chiral phase boundary, e.g. [97][98][99][100][101][102][103][104], the question of global baryon number conservation, e.g. [105][106][107], the inclusion of resonance decays, e.g.…”

Phenomenological study of the anisotropic quark matter in the 2-flavor Nambu-Jona-Lasinio model

“…[27,32]) that at higher baryon chemical potential, a first-order transition may exsit, which ends at a critical end point (CEP), which is of second order phase transition point. Furthermore, the effects of rotation [33,34], the magnetic field effects [35][36][37][38][39][40], finite-volume effects [41][42][43][44][45][46][47][48][49][50], non-extensive effects [51][52][53][54], external electric fields [55][56][57][58], the effects of chiral chemical potential [59][60][61][62] also have been considered in the effective models to provide a better insight in the QCD phase transition of a more realsitic QCD plasma.…”