Equation of State of the Strong Interaction Matter in an External Magnetic Field**Supported by the National Natural Science Foundation of China under Grant Nos. 10935001, 11175004 and 11435001, and the National Key Basic Research Program of China under Grant Nos. G2013CB834400 and 2015CB856900

Abstract

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.