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

TL;DR

This paper uses two-loop renormalization group calculations to analyze susceptibilities in a two-dimensional flat Fermi surface, revealing that only one susceptibility diverges at a time, with antiferromagnetic correlations dominating.

Contribution

It extends previous one-loop RG analyses by performing two-loop calculations, showing a different divergence pattern in susceptibilities for the flat Fermi surface.

Findings

All susceptibilities diverge at some energy scale.

Antiferromagnetic SDW correlations are the dominant instability.

Only one susceptibility diverges at a time in two-loop order.

Abstract

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.