Finite Isospin Chiral Perturbation Theory in a Magnetic Field

TL;DR

This paper investigates the phase diagram of finite isospin QCD with pions in a magnetic field using chiral perturbation theory, revealing type-II superconductor behavior and phase transitions between superconducting, vortex, and normal states.

Contribution

It provides a detailed analysis of the phase transitions and critical magnetic fields in finite isospin QCD within the framework of chiral perturbation theory, including numerical determination of transition points.

Findings

System behaves as a type-II superconductor.

Identified phases: uniform superconducting, vortex, and normal.

Numerically found critical magnetic field for phase transition.

Abstract

The phase diagram of finite isospin, zero temperature QCD with the pions coupled to photons in a uniform external magnetic field is explored in the low field, small isospin density regime for which chiral perturbation theory is a valid description. For realistic pion masses, the system behaves as a type-II superconductor: a uniform superconducting state is formed at low-enough magnetic fields, a vortex state for intermediate magnetic fields and finally a normal state for large magnetic fields. In each these phases (including the vortex phase), the $\pi^{0}$ remains uncondensed just as in the zero-external field problem. The critical magnetic field where the phase transition from the uniform superconducting state to a vortex state occurs was found numerically.