Impact of eight-quark interactions in chiral phase transitions I: Secondary magnetic catalysis

Abstract

The influence of a constant magnetic field on the order parameter of the four-dimensional Nambu and Jona-Lasinio model extended by the 't Hooft six-quark term and eight-quark interactions is considered. It is shown that the multi-quark interactions cause the order parameter to increase sharply (secondary magnetic catalysis) with increasing strength of the field at the characteristic scale $H\sim 10^{14}{\Lambda }^2$ G/MeV^2.

3 pages, prepared for the XIII International Conference on Selected Problems of Modern Theoretical Physics (SPMTP08), Bogoliubov Laboratory of Theoretical Physics, Dubna, Russia, June 23-27, 2008