Magnetic catalysis of a finite-size pion condensate

We study the Bose-Einstein condensation of a finite-size pion gas subject to the influence of a magnetic field. We find the expressions for the critical chemical potential and temperature for the onset of condensation. We show that for values of the external magnetic flux larger than the elemental flux, the critical temperature is larger than the one obtained by considering only finite-size effects. We use experimentally reported values of pion source sizes and multiplicities at Large Hadron Collider (LHC) energies to show that if the magnetic flux, produced initially in peripheral heavy-ion collisions, is at least partially preserved up to the hadronic phase, the combined finite-size and magnetic field effects give rise to a critical temperature above the kinetic freeze-out temperature. We discuss the implications for the evolution of the pion system created in relativistic heavy-ion collisions.