Critical scaling in the $N=1$ Thirring Model in $(2+1)d$

TL;DR

This paper investigates the critical behavior of the N=1 Thirring model in 2+1 dimensions using lattice simulations, revealing critical exponents consistent with analytic predictions and exploring the existence of a UV-stable fixed point.

Contribution

It provides the first lattice simulation results for N=1 using Wilson kernel domain wall fermions, and compares critical exponents with analytic Schwinger-Dyson solutions.

Findings

Critical exponents differ from previous estimates.

Exponents align with analytic Schwinger-Dyson predictions.

Preliminary results for N=2 suggest a critical flavor number.

Abstract

The Thirring model in 2+1$d$ with $N$ Dirac flavors can exhibit spontaneous U($2N)\to$U($N)\otimes$U($N$) breaking through fermion - antifermion condensation in the limit $m\to0$. With no small parameter in play the symmetry-breaking dynamics is strongly-interacting and quantitative work requires a fermion formulation accurately capturing global symmetries. We present simulation results for $N=1$ obtained with Wilson kernel domain wall fermions on $16^3\times L_s$, with $L_s=24,\ldots,120$. The $L_s\to\infty$ extrapolation of the bilinear condensate $\langle\bar\psi\psi\rangle$ as a function of coupling and bare mass is fitted to an empirical equation of state; the resulting critical exponents are significantly altered from previously obtained values, and for the first time resemble those emerging from analytic predictions based on approximate solutions to Schwinger-Dyson equations, consistent with a putative UV-stable renormalisation group fixed point. To address the non-perturbative issue of the value $N_c$ below which such a fixed point exists we present preliminary results obtained with $N=2$.