Effect of external magnetic fields on nucleon mass in a hot and dense medium: Inverse magnetic catalysis in the Walecka model

The vacuum to nuclear matter phase transition is studied in the presence of a constant external background magnetic field with the mean-field approximation in the Walecka model. The anomalous nucleon magnetic moment is taken into account using the modified "weak" field expansion of the fermion propagator with nontrivial correction terms for both charged and neutral particles. The effect of the nucleon magnetic moment is found to favor the magnetic catalysis effect at zero temperature and zero baryon density. However, extending the study to finite temperatures, it is observed that the anomalous nuclear magnetic moment plays a crucial role in characterizing the qualitative behavior of the vacuum to nuclear matter phase transition even in the case of weak external magnetic fields. The critical temperature corresponding to the vacuum to nuclear medium phase transition is observed to decrease with the external magnetic field, which can be identified as inverse magnetic catalysis in the Walecka model, whereas the opposite behavior is obtained in the case of a vanishing magnetic moment, indicating magnetic catalysis.