Absence of coexisting phase of quark-antiquark and diquark condensed phases in the extended Gross-Neveu model in $2 + 1$ dimensions

Abstract

We show that the coexisting phase of quark-antiquark and diquark condensed phases is absent in the cold quark matter in the $2 + 1$ dimensional extended Gross-Neveu model, which is in sharp contrast to the case of $3 + 1$ dimensional Nambu--Jona-Lasinio model.