We establish the FKG correlation inequality for the Euclidean scalar Yukawa_2 quantum field model and, when the Fermi mass is zero, for pseudoscalar Yukawag. To do so we approximate the quantum field model by a lattice spin system and show that the FKG inequality for this system follows from a positivity condition on the fundamental solution of the Euclidean Dirac equation with external field. We prove this positivity condition by applying the Vekua-Bers theory of generalized analytic functions.