  We study the phase diagram of quark matter at finite temperature (T) and
finite chemical potential (mu) in the strong coupling limit of lattice QCD for
color SU(3). We derive an analytical expression of the effective free energy as
a function of T and mu, including baryon effects. The finite temperature
effects are evaluated by integrating over the temporal link variable exactly in
the Polyakov gauge with anti-periodic boundary condition for fermions. The
obtained phase diagram shows the first order phase transition at low
temperatures and the second order phase transition at high temperatures
separated by the tri-critical point in the chiral limit. Baryon has effects to
reduce the effective free energy and to extend the hadron phase to a larger mu
direction at low temperatures.
