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.
Large-N_f chiral transition in the Yukawa model / S. Caracciolo, B. M. Mognetti, A. Pelissetto. - In: NUCLEAR PHYSICS. B. - ISSN 0550-3213. - 741:3(2006), pp. 421-440. [10.1016/j.nuclphysb.2006.02.029]
Large-N_f chiral transition in the Yukawa model
S. CaraccioloPrimo
;B.M. MognettiSecondo
;
2006
Abstract
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.Pubblicazioni consigliate
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