Spectroscopy, Equation Of State And Monopole Percolation In Lattice QED With Two Flavors

TL;DR

This study uses lattice QED simulations with two light quark flavors to investigate phase transitions, monopole condensation, and chiral symmetry breaking, revealing critical behavior consistent with four-dimensional percolation and deviations from mean field theory.

Contribution

It provides new numerical evidence on the critical point, monopole condensation, and chiral symmetry restoration in lattice QED with two flavors, including detailed critical exponents and mass ratios.

Findings

Critical point at β=0.225(5) with coincident monopole and chiral transitions.

Monopole condensation follows finite size scaling with four-dimensional percolation exponents.

Chiral exponents deviate from mean field expectations, indicating non-trivial critical behavior.

Abstract

Non-compact lattice QED with two flavors of light dynamical quarks is simulated on $16^4$ lattices, and the chiral condensate, monopole density and susceptibility and the meson masses are measured. Data from relatively high statistics runs at relatively small bare fermion masses of 0.005, 0.01, 0.02 and 0.03 (lattice units) are presented. Three independent methods of data analysis indicate that the critical point occurs at $\beta =0.225(5)$ and that the monopole condensation and chiral symmetry breaking transitions are coincident. The monopole condensation data satisfies finite size scaling hypotheses with critical indices compatible with four dimensional percolation. The best chiral equation of state fit produces critical exponents ($\delta=2.31$, $\beta_{mag}=0.763$) which deviate significantly from mean field expectations. Data for the ratio of the sigma to pion masses produces an estimate of the critical index $\delta$ in good agreement with chiral condensate measurements. In the strong coupling phase the ratio of the meson masses are $M_\sigma^2/M_\rho^2\approx 0.35$, $M_{A_1}^2/M_\rho^2\approx 1.4$ and $M_\pi^2/M_\rho^2\approx 0.0$, while on the weak coupling side of the transition $M_\pi^2/M_\rho^2\approx 1.0$, $M_{A_1}^2/M_\rho^2\approx 1.0$, indicating the restoration of chiral symmetry.\footnote{$\,^{}$}{August 1992}