Critical behavior of the (2+1)-dimensional Thirring model

TL;DR

This paper studies the phase transition and critical behavior of the (2+1)-dimensional Thirring model, focusing on chiral symmetry breaking, critical exponents, and the influence of flavor number using the functional renormalization group.

Contribution

It provides the first detailed analysis of the critical flavor number and associated phase transition in the Thirring model using dynamical bosonization within the functional RG framework.

Findings

Critical flavor number Nfc ~ 5.1 with systematic error ~1.

Computed critical exponents for the second order phase transition.

Identified quantum critical behavior in the many-flavor transition.

Abstract

We investigate chiral symmetry breaking in the (2+1)-dimensional Thirring model as a function of the coupling as well as the Dirac flavor number Nf with the aid of the functional renormalization group. For small enough flavor number Nf < Nfc, the model exhibits a chiral quantum phase transition for sufficiently large coupling. We compute the critical exponents of this second order transition as well as the fermionic and bosonic mass spectrum inside the broken phase within a next-to-leading order derivative expansion. We also determine the quantum critical behavior of the many-flavor transition which arises due to a competition between vector and chiral-scalar channel and which is of second order as well. Due to the problem of competing channels, our results rely crucially on the RG technique of dynamical bosonization. For the critical flavor number, we find Nfc ~ 5.1 with an estimated systematic error of approximately one flavor.