Symmetry nonrestoration in a Gross-Neveu model with a random chemical potential - art. no. 085014

We study the symmetry behavior of the Gross-Neveu model in three and two di mensions with a random chemical potential. This is equivalent to a four-fer mion model with charge conjugation symmetry as well as Z(2) chiral symmetry . At high temperature the Z(2) chiral symmetry is always restored. In three dimensions the initially spontaneously broken charge conjugation symmetry is not restored at high temperature, irrespective of the value of the disor der strength. In two dimensions and at zero temperature the charge conjugat ion symmetry undergoes a quantum phase transition from a symmetric state (f or weak disorder) to a broken state (for strong disorder) as the disorder s trength is varied. For any given value of disorder strength, the high-tempe rature behavior of the charge conjugation symmetry is the same as its zero- temperature behavior. Therefore, in two dimensions and for strong disorder strength the charge conjugation symmetry is not restored at high temperatur e.