  The phase structure of four-fermion theories is thoroughly investigated with
varying temperature and chemical potential for arbitrary space-time dimensions
$(2 \leq D < 4)$ by using the 1/N expansion method. It is shown that the chiral
symmetry is restored in the theory under consideration for sufficiently high
temperature and/or chemical potential. The critical line dividing the symmetric
and broken phase is given explicitly. It is found that for space-time dimension
$2 \leq D < 3$ both the first-order and second-order phase transition occur
depending on the value of temperature and chemical potential while for $3 \leq
D < 4$ only the second-order phase transition exists.

High Energy Physics - Phenomenology;High Energy Physics - Theory