Phase Structure of Four-Fermion Theories at Finite Temperature and Chemical Potential in Arbitrary Dimensions

The phase structure of four-fermion theories is thoroughly investigated with varying temperature and chemical potential for arbitrary space-time dimensions (2 ≤ 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 ≤ D < 3 both the first-order and second-order phase transition occur depending on the value of temperature and chemical potential while for 3 ≤ D < 4 only the second-order phase transition exists.