Scale-Dependent Analysis of Phase Structures in Two- and Four-Dimensional Fermion Models

Abstract

The structure of vacuum is studied in twoand four-dimensional fermion models by means of a resolution-dependent analysis which is proposed by Ezawa and Iwazaki. We first make the resolution-dependent analysis of the Gross-Neveu model based on the mean field expansion technique. Then we generalize this method to four dimensional models. As fermion models in two and four dimensions, we analyze a discrete and a continuous chiral invariant model (the Nambu-Jona-Lasinio model). In these models, we find that the discrete or the continuous symmetry breakdown occurs dynamically only at a long distance scale. The vacuum undergoes a second order phase transition in resolution R; for R Rc it is in an ordered phase. In four dimensions resolution R has a lower limit Rp-1=A (a cutoff parameter) because the four-dimensional fermion models are cutoff dependent theories.