Quark mass dependence of the QCD temperature transition in magnetic fields

Vacuum energy of quarks participates in the pressure balance at the temperature transition T_c and defines the dependence of T_c on m_q. We first check this dependence in absence of magnetic fields eB vs known lattice data, and then take into account the known strong dependence of the quark condensate on eB. The resulting function T_c(eB, m_q) is valid for all eB, m_q< \sqrt\sigma and explains the corresponding lattice data.