Universality of a Critical Magnetic Field in a Holographic Superconductor

We study aspects of holographic superconductors analytically in the presence of a constant external magnetic field. It is shown that the critical temperature and the critical magnetic field can be calculated at nonzero temperature. We detect the Meissner effect in such superconductors. A universal relation between black hole mass M and critical magnetic field H_c is proposed to be H_c/M^2/3≤0.687365. We also discuss some aspects of phase transition in terms of black hole entropy and Bekenstein's entropy to the energy upper bound.