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Anomalous magnetic moment of hot quarks, inverse magnetic catalysis and reentrance of chiral symmetry broken phase

The effect of anomalous magnetic moment of quarks on thermodynamic properties of the chiral condensate is studied, using of a two-flavor Nambu--Jona-Lasinio model at finite temperature $T$, chemical potential $μ$, and in the presence of a uniform magnetic field $eB$. To this purpose, the Schwinger linear-in-$B$ ansatz for the quark anomalous magnetic moment in term of the nonperturbative Bohr magneton is considered. In a two-dimensional flavor space, it leads to the correction $\hat{T}_{Sch}=\hatκ\hat{Q} eB$ in the energy dispersion relation of quarks. Here, $\hat{Q}$ is the quark charge matrix. We consider three different sets for $\hatκ$, and numerically determine the dependence of the constituent quark mass on $T,μ$ and $eB$ for fixed $\hatκ$. By exploring the complete phase portrait of this model in $T$-$μ$, $μ$-$eB$, and $T$-$eB$ phase spaces for various fixed $eB$, $T$, $μ$ and $\hatκ$, we observe that inverse magnetic catalysis occurs for large enough $\hatκ$. Moreover, in the regime of weak magnetic fields, the phenomenon of reentrance of chiral symmetry broken and restored phases occurs for $T, μ$ and $eB$ dependent $\hatκ$.