Finite-volume analysis of N_f-induced chiral phase transitions

TL;DR

This paper analyzes how the spectrum of the Dirac operator in Euclidean QCD on a torus can be used to study chiral phase transitions as the number of flavors N_f increases, with implications for lattice simulations.

Contribution

It introduces a finite-volume approach using inverse moments of Dirac eigenvalues to detect chiral phase transitions in lattice QCD simulations.

Findings

Large-volume dependence relates to chiral order parameters.

Dirac inverse moments can distinguish phase transitions.

Method aids in identifying quark condensate suppression.

Abstract

In the framework of Euclidean QCD on a torus, we study the spectrum of the Dirac operator through inverse moments of its eigenvalues, averaged over topological sets of gluonic configurations. The large-volume dependence of these sums is related to chiral order parameters. We sketch how these results may be applied to lattice simulations in order to investigate the chiral phase transitions occurring when N_f increases. In particular, we demonstrate how Dirac inverse moments at different volumes could be compared to detect in a clean way the phase transition triggered by the suppression of the quark condensate and by the enhancement of the Zweig-rule violation in the vacuum channel.