  We study effective models of chiral fields and Polyakov loop expected to
describe the dynamics responsible for the phase structure of two-flavor QCD at
finite temperature and density. We consider chiral sector described either
using linear sigma model or Nambu-Jona-Lasinio model and study the phase
diagram and determine the location of the critical point as a function of the
explicit chiral symmetry breaking (i.e. the bare quark mass $m_q$). We also
discuss the possible emergence of the quarkyonic phase in this model.
