The Kramers equation simulation algorithm II. An application to the Gross-Neveu model

TL;DR

This paper compares the Kramers equation simulation algorithm with the Hybrid Monte Carlo method in simulating the two-dimensional lattice Gross-Neveu model, demonstrating comparable performance and improved numerical safety of the Kramers approach.

Contribution

It introduces a comparison between the Kramers equation algorithm and Hybrid Monte Carlo for lattice field theory simulations, highlighting the Kramers method's numerical stability.

Findings

Both algorithms accurately determine the critical mass.

Results from both methods agree within errors.

Kramers algorithm shows better numerical safety.

Abstract

We continue the investigation on the applications of the Kramers equation to the numerical simulation of field theoretic models. In a previous paper we have described the theory and proposed various algorithms. Here, we compare the simplest of them with the Hybrid Monte Carlo algorithm studying the two-dimensional lattice Gross-Neveu model. We used a Symanzik improved action with dynamical Wilson fermions. Both the algorithms allow for the determination of the critical mass. Their performances in the definite phase simulations are comparable with the Hybrid Monte Carlo. For the two methods, the numerical values of the measured quantities agree within the errors and are compatible with the theoretical predictions; moreover, the Kramers algorithm is safer from the point of view of the numerical precision.