Monopole Percolation and The Universality Class of the Chiral Transition in Four Flavor Noncompact Lattice QED

TL;DR

This study investigates the chiral transition in four flavor noncompact lattice QED, revealing a monopole percolation transition in the universality class of four-dimensional percolation and supporting a power-law behavior of the chiral condensate.

Contribution

The paper provides the first detailed simulation evidence linking monopole percolation to the chiral transition in four-flavor noncompact lattice QED, including precise measurements and analysis of critical behavior.

Findings

Transition occurs at β ≈ 0.205 with critical behavior in 4D percolation universality class.

Chiral condensate exhibits power-law behavior consistent with a second-order transition.

Predicted mass ratio m_π^2/m_σ^2 aligns with spectrum calculations.

Abstract

We simulate four flavor noncompact lattice QED using the Hybrid Monte Carlo algorithm on $10^4$ and $16^4$ lattices. Measurements of the monopole susceptibility and the percolation order parameter indicate a transition at $\beta = {1/e^2} = .205(5)$ with critical behavior in the universality class of four dimensional percolation. We present accurate chiral condensate measurements and monitor finite size effects carefully. The chiral condensate data supports the existence of a power-law transition at $\beta = .205$ in the same universality class as the chiral transition in the two flavor model. The resulting equation of state predicts the mass ratio $m_\pi^2/m_\sigma^2$ in good agreement with spectrum calculations while the hypothesis of a logarithmically improved mean field theory fails qualitatively.