https://doi.org/10.1140/epja/s10050-021-00491-y
Review
QCD phase diagram in a constant magnetic background
Inverse magnetic catalysis: where models meet the lattice
Department of Physics, Norwegian University of Science and Technology, Høgskoleringen 5, 7491, Trondheim, Norway
Received:
27
February
2021
Accepted:
13
May
2021
Published online:
9
June
2021
Magnetic catalysis is the enhancement of a condensate due to the presence of an external magnetic field. Magnetic catalysis at 
is a robust phenomenon in low-energy theories and models of QCD as well as in lattice simulations. We review the underlying physics of magnetic catalysis from both perspectives. The quark-meson model is used as a specific example of a model that exhibits magnetic catalysis. Regularization and renormalization are discussed and we pay particular attention to a consistent and correct determination of the parameters of the Lagrangian using the on-shell renormalization scheme. A straightforward application of the quark-meson model and the NJL model leads to the prediction that the chiral transition temperature 
is increasing as a function of the magnetic field B. This is in disagreement with lattice results, which show that is a decreasing function of B, independent of the pion mass. The behavior can be understood in terms of the so-called valence and sea contributions to the quark condensate and the competition between them. We critically examine these ideas as well recent attempts to improve low-energy models using lattice input.
© The Author(s) 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
