Evaluation of the Bilinear Condensate of the Planar Thirring Model in the Strongly Coupled Region

TL;DR

This paper investigates the bilinear condensate in the strongly coupled critical region of the planar Thirring model, using improved Dirac operators and numerical methods to characterize its phase transition and critical exponents.

Contribution

It introduces enhanced computational techniques with overlap and domain wall Dirac operators to accurately evaluate the condensate and critical behavior in the model.

Findings

Successful calculation of the bilinear condensate in the critical region.

Determination of the equation of state and critical exponents.

Comparison of different Dirac operators for numerical stability.

Abstract

The planar Thirring model is thought to have a strongly coupled critical point for a single flavour of fermion. We look at the calculation of the bilinear condensate in this critical region, and its characterisation via an equation of state. Since the computation is numerically challenging we investigate improved Dirac operators. We present findings on different methods of calculation using a rational hybrid Monte Carlo scheme, and calculations of the bilinear condensate, an equation of state, and the associated critical exponents. Overlap and domain wall Dirac operators, and variants therein are considered.