Relation between the Polyakov loop and the chiral order parameter at strong coupling

We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature by using the Gocksch-Ogilvie model with fundamental or adjoint quarks. The model is based on the double expansion of strong coupling and large dimensionality on the lattice. In an analytic way with the mean field approximation employed, we show that the confined phase must be accompanied by the spontaneous breaking of the chiral symmetry for both fundamental and adjoint quarks. Then we proceed to numerical analysis to look into the coupled dynamics of the Polyakov loop and the chiral order parameter. In the case of fundamental quarks, the pseudo-critical temperature inferred from the Polyakov loop behavior turns out to coincide with the pseudo-critical temperature of the chiral phase transition. We discuss the physical implication of the coincidence of the pseudo-critical temperatures in two extreme cases; one is the deconfinement dominance and the other is the chiral dominance. As for adjoint quarks, the deconfinement transition of first order persists and the chiral phase transition occurs distinctly at higher temperature than the deconfinement transition does. The present model study gives us a plausible picture to understand the results from the lattice QCD and aQCD simulations.