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, using the mean field approximation, we show that the confined phase must be accompanied by the spontaneous breaking of chiral symmetry for both fundamental and adjoint quarks. Then we proceed to numerical analyses to look into the coupled dynamics of the Polyakov loop and the chiral order parameter. In the case of fundamental quarks, the pseudocritical temperature inferred from the Polyakov loop behavior turns out to coincide with the pseudocritical temperature of the chiral phase transition. We discuss the physical implication of the coincidence of the pseudocritical temperatures in two extreme cases: one is deconfinement dominance and the other is chiral dominance. As for adjoint quarks, the deconfinement transition of first order persists and the chiral phase transition occurs at distinctly higher temperature than the deconfinement transition. The present model study gives us a plausible picture to understand the results from lattice QCD and aQCD simulations.