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We perform the renormalization group analysis on the dynamical symmetrybreaking under strong external magnetic field, studied recently by Gusynin,Miransky and Shovkovy. We find that any attractive four-Fermi interactionbecomes strong in the low energy, thus leading to dynamical symmetry breaking.When the four-Fermi interaction is absent, the $\beta$-function for theelectromagnetic coupling vanishes in the leading order in $1/N$. By solving theSchwinger-Dyson equation for the fermion propagator, we show that in $1/N$expansion, for any electromagnetic coupling, dynamical symmetry breaking occursdue to the presence of Landau energy gap by the external magnetic field.Comment: 11pages, late

RG analysis of magnetic catalysis in dynamical symmetry breaking