On the magnetic catalysis and inverse catalysis of phase transitions in the linear sigma model

TL;DR

This paper investigates how magnetic fields influence phase transitions in the linear sigma model, revealing magnetic catalysis for pion condensates and inverse catalysis for chiral restoration, aligning with recent lattice results.

Contribution

It provides a detailed analysis of magnetic effects on phase transitions in the linear sigma model, including beyond one-loop corrections and plasma screening effects.

Findings

High magnetic fields increase the critical temperature for pion condensate formation.

Magnetic fields decrease the chiral transition temperature, showing inverse catalysis.

Results agree with recent lattice QCD findings.

Abstract

We consider the evolution of critical temperature both for the formation of a pion condensate as well as for the chiral transition, from the perspective of the linear sigma model, in the background of a magnetic field. We developed the discussion for the pion condensate in one loop approximation for the effective potential getting magnetic catalysis for high values of B, i.e. a raising of the critical temperature with the magnetic field. For the analysis of the chiral restoration, we go beyond this approximation, by taking one loop thermo-magnetic corrections to the couplings as well as plasma screening effects for the boson's masses, expressed through the resumation of ring diagrams. Here we found the opposite behavior, i.e. inverse magnetica catalysis, i.e. a decreasing of the chiral critical temperature as function of the intensity of the magnetic field, which seems to be in agreement with recent results form the lattice community.