Information theoretical view of QCD effective model with heavy quarks

To understand the phase transition phenomena, information theoretical approaches can pick up some important properties of the phenomena based on the probability distribution. In this paper, we show information theoretical aspects of the three-dimensional three-state Potts model with the external field which is corresponded to the QCD effective model with heavy quarks. The transfer mutual information which represents the information flow of two spin variables is numerically estimated based on the Markovchain Monte Carlo method. The transfer mutual information has the peak near the confinementdeconfinement transition, and it may be used to detect the precursors of the transition. Since the transfer mutual information still has the peak even if the Polyakov-loop changes continuously and smoothly, we may pick up some aspects of the confinement-deconfinement nature from the information flow properties. Particularly, the transfer mutual information shows the significantly different behavior below and above the Roberge-Weiss endpoint existed in the pure imaginary chemical potential region, which may indicate the system change by the confinement-deconfinement transition.

Automated summary

This paper investigates the information theoretical aspects of the three-dimensional three-state Potts model with external field, finding a peak in information flow near the confinement-deconfinement transition which can be used to detect precursors of the transition. The transfer mutual information still exhibits a peak even with continuous changes in the Polyakov-loop, suggesting the potential to identify aspects of the confinement-deconfinement nature from information flow properties. Additionally, significant differences in behavior below and above the Roberge-Weiss endpoint in the region of pure imaginary chemical potential indicate a system change through the confinement-deconfinement transition.