Finite isospin chiral perturbation theory in a magnetic field

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 sufficiently low magnetic fields, a vortex state for intermediate magnetic fields, and finally a normal state for large magnetic fields. In each of these phases (including the vortex phase), 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.