UV fixed-point structure of the three-dimensional Thirring model

TL;DR

This paper uses the functional renormalization group to analyze the UV fixed-point structure of the three-dimensional Thirring model, revealing multiple fixed points and potential new universality classes related to phase transitions.

Contribution

It provides a comprehensive classification of four-fermion interactions and identifies multiple fixed points, including the conventional Thirring fixed point and new candidates for universality classes.

Findings

The UV fixed point lies in a two-dimensional coupling plane.

The Thirring fixed point persists at finite Nf with one relevant direction.

Two additional fixed points suggest new universality classes.

Abstract

We investigate the UV fixed-point structure of the three-dimensional Thirring model by means of the functional renormalization group (RG). We classify all possible 4-fermi interactions compatible with the present chiral and discrete symmetries and calculate the purely fermionic RG flow using a full basis of fermionic four-point functions in the point-like limit. Our results show that the UV complete (asymptotically safe) Thirring model lies in a two-dimensional coupling plane which reduces to the conventional Thirring coupling only in the strict large-Nf limit. In addition to the Thirring universality class which is characterized by one relevant direction (also at finite Nf), two further interacting fixed points occur which may define new universality classes of second-order phase transitions also involving parity-broken phases. The Nf-dependence of the Thirring fixed point sheds further light on the existence of an Nf-controlled quantum phase transition above which chiral symmetry remains unbroken for arbitrary large coupling, even though a definite answer will require a direct computation of competing orders.