Phase diagram for charged scalars in a magnetic field at finite temperature

TL;DR

This paper studies how magnetic fields influence the phase transition of charged scalars with spontaneous symmetry breaking, revealing a shift from first to second order and a decrease in critical temperature with increasing magnetic field.

Contribution

It introduces a method to compute magnetic and thermal corrections for charged scalars at high temperature and strong magnetic fields, clarifying the phase transition nature.

Findings

Phase transition is first order at low magnetic fields.

Transition becomes second order as magnetic field increases.

Critical temperature decreases with magnetic field presence.

Abstract

We investigate the nature of the phase transition for charged scalars in the presence of a magnetic background for a theory with spontaneous symmetry breaking. We perform a careful treatment of the negative mass squared as a function of the order parameter and present a suitable method to obtain magnetic and thermal corrections up to ring order for the high temperature limit and the case where the magnetic field strength is larger than the absolute value of the square of the mass parameter. We show that for a given value of the self-coupling, the phase transition is first order for a small magnetic field strength and becomes second order as this last grows. We also show that the critical temperature in the presence of the magnetic field is always below the critical temperature for the case where the field is absent.