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.

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Thermodynamic formulas for investigating systems with density and/or temperature dependent particle masses are generally derived from the fundamental derivation equality of thermodynamics. Various problems in the previous treatments are discussed and modified. Properties of strange quark matter in bulk and strangelets at both zero and finite temperature are then calculated based on the new thermodynamic formulas with a new quark mass scaling, which indicates that low mass strangelets near β equilibrium are multi-quark states with an anti-strange quark, such as the pentaquark (u 2 d 2s ) for baryon nmber 1 and the octaquark (u 4 d 3s ) for dibaryon etc.