Renormalization Group And Scaling Within The Microcanonical Fermionic Average Approach

TL;DR

This paper introduces a method using the Microcanonical Fermionic Average approach to study renormalization group flows and scaling in lattice gauge theories, demonstrated on the Schwinger Model, with potential applications to more realistic theories.

Contribution

It develops a novel technique to extract renormalization group trajectories and scaling functions without computing fermionic determinants at each parameter point.

Findings

Successfully applied to the Schwinger Model

Extracted renormalization group trajectories

Discussed applicability to realistic theories

Abstract

The MFA approach for simulations with dynamical fermions in lattice gauge theories allows in principle to explore the parameters space of the theory (e.g. the $\beta, m$ plane for the study of chiral condensate in QED) without the need of computing the fermionic determinant at each point. We exploit this possibility for extracting both the renormalization group trajectories ("constant physics lines") and the scaling function, and we test it in the Schwinger Model. We discuss the applicability of this method to realistic theories.