Magnetic catalysis is the enhancement of a condensate due to the presence of an external magnetic field. Magnetic catalysis at \(T=0\) 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 \(T_{\chi }\) is increasing as a function of the magnetic field B. This is in disagreement with lattice results, which show that \(T_{\chi }\) 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.

磁催化是由于外部磁场的存在而导致冷凝物的增强。\(T=0\)处的磁催化在QCD 的低能理论和模型以及晶格模拟中是一种稳健的现象。我们从两个角度回顾了磁催化的基础物理学。夸克介子模型用作展示磁催化的模型的具体示例。讨论了正则化和重整化，我们特别注意使用壳上重整化方案一致和正确地确定拉格朗日参数。夸克介子模型和 NJL 模型的直接应用导致预测手性转变温度\(T_{\chi }\)作为磁场B的函数增加。这与晶格结果不一致，晶格结果表明\(T_{\chi }\)是B的递减函数，与 pion 质量无关。这种行为可以从所谓的价态和海洋对夸克凝聚态的贡献以及它们之间的竞争来理解。我们批判性地研究了这些想法以及最近使用晶格输入改进低能量模型的尝试。