Three dimensional four-fermion models - A Monte Carlo study

TL;DR

This study uses Monte Carlo simulations to analyze three 3D four-fermion models with different chiral symmetries, revealing critical behavior and confirming analytical predictions.

Contribution

First high-precision Monte Carlo analysis of 3D four-fermion models with multiple chiral symmetries, including finite size scaling and critical exponent evaluation.

Findings

Identified second order chiral phase transitions in all models.

Detected next-to-leading order corrections consistent with large-N_f calculations.

Established the critical couplings as ultraviolet fixed points.

Abstract

We present results from numerical simulations of three different 3d four-fermion models that exhibit Z_2, U(1), and SU(2) x SU(2) chiral symmetries, respectively. We performed the simulations by using the hybrid Monte Carlo algorithm. We employed finite size scaling methods on lattices ranging from 8^3 to 40^3 to study the properties of the second order chiral phase transition in each model. The corresponding critical coupling defines an ultraviolet fixed point of the renormalization group. In our high precision simulations, we detected next-to-leading order corrections for various critical exponents and we found them to be in good agreement with existing analytical large-N_f calculations.