  We discuss the chiral symmetry restoration at high temperature and chemical
potential for a four-fermion interaction theory in arbitrary dimensions ($2\leq
D<4$). To investigate the ground state of the theory we calculate the effective
potential and the gap equation using the method of the $1/N$ expansion. We
study the phase structure at finite temperature and chemical potential and show
critical curves which divide the symmetric and asymmetric phase. We find that
the first and second order phase transition coexist for $2\leq D \leq 3$
depending on the value of the temperature and chemical potential. On the other
hand only the second order phase transition is realized for $3<D<4$. We also
present the critical behavior of the dynamically generated fermion mass. (Talk
presented at the Fourth International Workshop on Thermal Field Theory and
Their Application, Dalian, P. R. China, 5--10 August, 1995.)
