Abstract
We investigate the impact of finite volume and the corresponding restrictions on long-range correlations on the location of the critical endpoint in the QCD phase diagram. To this end, we employ a sophisticated combination of lattice Yang--Mills theory and a (truncated) version of Dyson--Schwinger equations in Landau gauge for $2+1$ quark flavors that has been studied extensively in the past. In the infinite-volume limit, this system predicts a critical endpoint at moderate temperature and large chemical potential. We study this system at small and intermediate volumes and determine the dependence of the location of the critical endpoint on the boundary conditions and the volume of a three-dimensional cube with edge length $L$. We demonstrate that noticeable volume effects of more than five percent occur only for $L\ensuremath{\lesssim}5\text{ }\text{ }\mathrm{fm}$ and that volumes as large as ${L}^{3}\ensuremath{\gtrsim}(8\text{ }\text{ }\mathrm{fm}{)}^{3}$ are very close to the infinite-volume limit.
Highlights
There are a number of reasons why finite-volume studies of the location and properties of a putative chiral critical endpoint (CEP) in the phase diagram of QCD are interesting
We investigate the impact of finite volume and the corresponding restrictions on long-range correlations on the location of the critical endpoint in the QCD phase diagram
For antiperiodic spatial boundary conditions (ABC) and PBCÃ, both phase diagrams show a similar trend when the box size is decreased: the CEP moves toward smaller temperatures and larger chemical potentials
Summary
There are a number of reasons why finite-volume studies of the location and properties of a putative chiral critical endpoint (CEP) in the phase diagram of QCD are interesting. Theoretical studies of finite-volume effects on the QCD phase diagram have been carried out in a number of approaches besides lattice QCD. We trace the location of the CEP in the QCD phase diagram for various volumes and determine the box size necessary to approach the infinitevolume results. We discuss volume effects on the curvature of the crossover line at small chemical potential and compare with lattice QCD.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
