2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192200We perform the renormalization group analysis on the dynamical symmetry breaking under strong external magnetic field, studied recently by Gusynin, Miransky and Shovkovy. We find that any attractive four-Fermi interaction becomes strong in the low energy, thus leading to dynamical symmetry breaking. When the four-Fermi interaction is absent, the $β$-function for the electromagnetic coupling vanishes in the leading order in $1/N$. By solving the Schwinger-Dyson equation for the fermion propagator, we show that in $1/N$ expansion, for any electromagnetic coupling, dynamical symmetry breaking occurs due to the presence of Landau energy gap by the external magnetic field.11pages, latexHigh Energy Physics - TheoryCondensed Mattertext