Chiral Disorder and Random Matrix Theory with Magnetism

TL;DR

This paper investigates the effects of magnetic fields on chiral disorder in QCD, using random matrix theory and lattice data to explore weak, strong, and ultra-strong magnetism regimes and their implications for the QCD phase diagram.

Contribution

It introduces a chiral random matrix effective action incorporating magnetism and matter, providing new insights into QCD phase transitions under magnetic influence.

Findings

Weak magnetism aligns with chiral perturbation theory.

Strong magnetism agrees with lattice QCD data.

Ultra-strong magnetism matches perturbative QCD expectations.

Abstract

We revisit the concept of chiral disorder in QCD in the presence of a QED magnetic field |eH|. Weak magnetism corresponds to |eH| < 1/rho^2 with rho\approx (1/3) fm the vacuum instanton size, while strong magnetism the reverse. Asymptotics (ultra-strong magnetism) is in the realm of perturbative QCD. We analyze weak magnetism using the concept of the quark return probability in the diffusive regime of chiral disorder. The result is in agreement with expectations from chiral perturbation theory. We analyze strong and ultra-strong magnetism in the ergodic regime using random matrix theory including the effects of finite temperature. The strong magnetism results are in agreement with the currently reported lattice data in the presence of a small shift of the Polyakov line. The ultra-strong magnetism results are consistent with expectations from perturbative QCD. We suggest a chiral random matrix effective action with matter and magnetism to analyze the QCD phase diagram near the critical points under the influence of magnetism.