Quark Antiscreening at Strong Magnetic Field and Inverse Magnetic   Catalysis
  The dependence of the QCD coupling constant with a strong magnetic field and the implications for the critical temperature of the chiral phase transition are investigated. It is found that the coupling constant becomes anisotropic in a strong magnetic field and that the quarks, confined by the field to the lowest Landau level where they pair with antiquarks, produce an antiscreening effect. These results lead to inverse magnetic catalysis, providing a natural explanation for the behavior of the critical temperature in the strong-field region. 
E. J. Ferrer, V. de la Incera, and X. J. Wen
nucl-th hep-ph