Large-N_f chiral transition in the Yukawa model

Details Large-N_f chiral transition in the Yukawa model Large-N_f chiral transition in the Yukawa model

2006-01-14

arxiv.org/abs/hep-lat/0601018v1

Nucl.Phys. B 741 (2006) 421-440

Physics

High Energy Physics

High Energy Physics - Lattice

Scientific paper

10.1016/j.nuclphysb.2006.02.029

We investigate the finite-temperature behavior of the Yukawa model in which $N_{f}$ fermions are coupled with a scalar field $\phi$ in the limit $N_f \to \infty$. Close to the chiral transition the model shows a crossover between mean-field behavior (observed for $N_f = \infty$) and Ising behavior (observed for any finite $N_f$). We show that this crossover is universal and related to that observed in the weakly-coupled $\phi^4$ theory. It corresponds to the renormalization-group flow from the unstable Gaussian fixed point to the stable Ising fixed point. This equivalence allows us to use results obtained in field theory and in medium-range spin models to compute Yukawa correlation functions in the crossover regime.

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