Information theoretical view of QCD effective model with heavy quarks

TL;DR

This paper applies information theoretical measures, specifically transfer mutual information, to the 3D 3-state Potts model with an external field, revealing insights into the confinement-deconfinement transition relevant to QCD with heavy quarks.

Contribution

It introduces the use of transfer mutual information to detect phase transitions in a QCD effective model, highlighting its potential to identify transition precursors and system changes.

Findings

Transfer mutual information peaks near the transition point.

It detects transition precursors even with smooth Polyakov-loop changes.

Different behaviors of information flow are observed across the Roberge-Weiss endpoint.

Abstract

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 3-dimensional 3-state Potts model with the external field which is corresponding 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 Markov-chain Monte-Carlo method. The transfer mutual information has the peak near the confinement-deconfinement transition, and it may be used to detect the precursors of the transition. Since the transfer mutual information still have 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.