Four - Fermi Theories in Fewer Than Four Dimensions
- Hands, S
- Kocic, Aleksandar
- Kogut, J B
DOIAbstract
Four-fermi models in dimensionality $2<d<4$ exhibit an ultra-violet stable renormalization group fixed point at a strong value of the coupling constant where chiral symmetry is spontaneously broken. The resulting field theory describes relativistic fermions interacting non-trivially via exchange of scalar bound states. We calculate the $O(1/N_f)$ corrections to this picture, where $N_f$ is the number of fermion species, for a variety of models and confirm their renormalizability to this order. A connection between renormalizability and the hyperscaling relations between the theory's critical exponents is made explicit. We present results of extensive numerical simulations of the simplest model for $d=3$, performed using the hybrid Monte Car...
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