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The Linear Sigma Model and the formation of a charged pion condensate in the presence of an external magnetic field
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We discuss the charged pion condensation phenomenon in the linear sigma model, in the presence of an external uniform magnetic field. The critical temperature is obtained as a function of the external magnetic field, assuming the transition is of second order, by considering a dilute gas at low temperature. As a result we found magnetic anti-catalysis in the Bose-Einstein condensation for lower values of the external magnetic field, and catalysis for higher values of the external magnetic field. This behavior confirms previous results with a single charged scalar field.
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Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field
In the linear sigma model with quarks, the neutral pion mass first falls and then rises as the external magnetic field grows, a nonmonotonic curve that the earlier weak-field calculation did not show.
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