  Coupling of `t Hooft's determinant term is investigated in the framework of
the three flavor linear sigma model as a function of the chiral condensate.
Using perturbation theory around the minimum point of the effective action, we
calculate the renormalization group flow of the first field dependent
correction to the coupling of the conventional U_A(1) breaking determinant
term. It is found that at low temperatures mesonic fluctuations make the
anomaly increase when the chiral condensate decreases. As an application, we
analyze the effect at the zero temperature nuclear liquid-gas transition.
