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 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 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 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.
Highlights
Understanding the confinement-deconfinement transition at finite temperature (T) and chemical potential (μ) in quantum chromodynamics (QCD) is one of the important and interesting subjects in elementary particle, nuclear, and hadron physics and astrophysics
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
We have investigated the information theoretical aspects of the confinement-deconfinement nature in the QCD effective model with heavy quarks; the three-dimensional three-state Potts model is employed
Summary
Understanding the confinement-deconfinement transition at finite temperature (T) and chemical potential (μ) in quantum chromodynamics (QCD) is one of the important and interesting subjects in elementary particle, nuclear, and hadron physics and astrophysics. In the ordinary understanding of the confinement-deconfinement transition at finite temperature in QCD with a vanishing chemical potential, there is no “phase transition,” and there is a crossover. In the confinement-deconfinement crossover, there are no singularities in the local order-parameters and the thermodynamic quantities. It has been recently discussed in Ref.
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