Phase diagram of the three dimensional Thirring model - A Monte Carlo study

TL;DR

This Monte Carlo study investigates the phase diagram of the 3D Thirring model, revealing a second order chiral phase transition at N_f=6 and estimating the critical flavor number around 6.5, contributing to understanding its continuum limit.

Contribution

The paper provides the first Monte Carlo simulation results for N_f=6, identifying a second order phase transition and estimating the critical flavor number, advancing the non-perturbative understanding of the model.

Findings

Second order chiral phase transition at N_f=6

Critical coupling corresponds to an ultra-violet fixed point

Estimated critical flavor number N_fc ≈ 6.5

Abstract

Certain approximate solutions of the continuum Schwinger-Dyson Equations (SDEs) predict chiral symmetry breaking in the 3d Thirring model when the number of fermion flavors N_f<4.32 whereas others predict symmetry breaking for all N_f. Our results from Monte Carlo simulations with N_f=6, predict a second order chiral phase transition. The critical coupling in this case corresponds to an ultra-violet fixed point of the renormalization group defining a non-trivial continuum limit. Further, our numerical simulations provide an estimate for the critical number of fermion flavors, N_fc \approx 6.5.