Large- chiral transition in the Yukawa model

Abstract

We investigate the finite-temperature behavior of the Yukawa model in which N f fermions are coupled with a scalar field φ in the limit N f → ∞. Close to the chiral transition the model shows a crossover between mean-field behavior (observed for N f = ∞) 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 φ 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.

Critical region of strong-coupling lattice QCD in different large-Nlimits

“…Combining the results of [3,10,11], and of our study here, we emphasize that the critical region in large-N phase transitions is suppressed only when the LGW effective action for the transition has an overall factor of N α , α > 0. This suppresses thermal fluctuations in the order parameter, and can make MF scaling exact.…”

“…The lattice symmetries are restored in a second order transition at the finite T c , whose critical behavior is closely related to the behavior seen in [1,3,10,11] for the systems studied there. We show that taking N f → ∞ before t ≡ |T − T c |/T c → 0, makes MF exponents exact.…”

“…that describes a stable ordered phase with q > 0 below T c = J, and a MF scaling q ∼ (T c − T ) 1/2 in its vicinity. Here we reach the same 'puzzle' as did [1,3,10,11] for the Gross-Neveu, Yukawa and classical 2D Heisenberg models: the result above is exact at N f = ∞, but for any finite N f it is wrong. There, the scaling of q is dictated by the symmetry breakdown, and by d. The resolution of this puzzle is that the critical region shrinks with N f [3,10,11].…”

“…Here we reach the same 'puzzle' as did [1,3,10,11] for the Gross-Neveu, Yukawa and classical 2D Heisenberg models: the result above is exact at N f = ∞, but for any finite N f it is wrong. There, the scaling of q is dictated by the symmetry breakdown, and by d. The resolution of this puzzle is that the critical region shrinks with N f [3,10,11]. We now turn to show how this happens for our model.…”

Composite boson dominance in relativistic field theories

“…The effective action we derived can be used in the study of QCD by numerical simulations and, we hope, by a perturbative expansion along the lines of [11] and by keeping into account the subtleties related to the 1/N f expansion [20]. In this case the effective bosons carry obviously the quantum numbers of the chiral mesons and chiral symmetry is broken by the condensation of the sigma-meson.…”