Fixed Point Four-Fermi Theories

Abstract

I review dynamical chiral symmetry breaking in four-fermi models, including results of Monte Carlo simulations with dynamical fermions. For 2<d<4, where the phase transition defines an ultraviolet fixed point of the renormalisation group, the continuum theory may either be describable using the large-N_f expansion, as in the case of the Gross-Neveu model, or be intrinsically non-perturbative, as in the case of the Thirring model. For d=4, the models are trivial and are described by a mean field equation of state with logarithmic corrections to scaling, which may nonetheless define new universality classes distinct from those of ferromagnetism.