Short-Range Order in a Flat Two-Dimensional Fermi Surface

We present the two-loop renormalization group (RG) calculations of all the susceptibilities associated with the two-dimensional flat Fermi surface with rounded corners (FS). Our approach follows our fermionic field theory RG method presented in detail earlier on. In one loop order our calculation reproduce the results obtained previously by other RG schemes. All susceptibilities diverge at some energy scale and the antiferromagnetic SDW correlations produce indeed the dominant instability in the physical system. In contrast, in two-loop order, for a given initial set of values of coupling constant regime only one of the susceptibilities at a time seems to diverge.