Fermionic functional renormalization group for first-order phase transitions: a mean-field model

TL;DR

This paper introduces a counterterm technique within the fermionic functional renormalization group to detect and analyze first-order phase transitions and metastable states in many-fermion systems, overcoming limitations of standard RG methods.

Contribution

The authors develop a counterterm method in fRG that enables the study of first-order transitions and metastable states, which are typically inaccessible with standard susceptibility analysis.

Findings

Successfully detects first-order phase transitions and metastable states.

Reproduces standard results for continuous transitions.

Avoids large interactions away from critical temperature.

Abstract

First-order phase transitions in many-fermion systems are not detected in the susceptibility analysis of common renormalization-group (RG) approaches. Here we introduce a counterterm technique within the functional renormalization-group (fRG) formalism which allows access to all stable and metastable configurations. It becomes possible to study symmetry-broken states which occur through first-order transitions as well as hysteresis phenomena. For continuous transitions, the standard results are reproduced. As an example, we study discrete-symmetry breaking in a mean-field model for a commensurate charge-density wave. An additional benefit of the approach is that away from the critical temperature for the breaking of discrete symmetries large interactions can be avoided at all RG scales.