Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2005-09-20
PoS LAT2005 (2005) 187
Physics
High Energy Physics
High Energy Physics - Lattice
Talk presented at XXIIIrd International Symposium on Lattice Field Theory, 25-30 July 2005, Trinity College, Dublin, Ireland
Scientific paper
We investigate the Yukawa model in which $N_f$ fermions are coupled with a scalar field $\phi$ through a Yukawa interaction. The phase diagram is rather well understood. If the fermions are massless, there is a chiral transition at $T_c$: for $T < T_c$ chiral symmetry is spontaneously broken. At $N_f=\infty$ the transition is mean-field like, while, for any finite $N_f$, standard arguments predict Ising behavior. This apparent contradiction has been explained by Kogut et al., who showed by scaling arguments and Monte Carlo simulations that in the large-$N_f$ limit the width of the Ising critical region scales as a power of $1/N_f$, so that only mean-field behavior is observed for $N_f$ strictly equal to infinity. We will show how the results of Kogut et al. can be recovered analytically in the framework of a generalized $1/N_f$ expansion. The method we use is a simple generalization of the method we have recently applied to a two-dimensional generalized Heisenberg model.
Caracciolo Sergio
Mognetti Bortolo Matteo
Pelissetto Andrea
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