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Equation of State of the Strong Interaction Matter in an External Magnetic Field

We investigate the equation of state of the strong interaction matter in a background magnetic field via the two flavor Nambu–Jona-Lasinio model. Starting from the mean-field thermodynamical potential density Ω, we calculate the pressure density p, the entropy density s, the energy density ϵ, and the interaction measure (ϵ − 3p)/T4 of the strong interaction matter at finite temperature and finite magnetic field. The results manifest that the chiral phase transition is just a crossover but not a low order phase transition. Moreover there may exist magnetic catalysis effect, and its mechanism is just the effective dimension reduction induced by the magnetic field.