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

Perturbative RG analysis of the condensate dependence of the axial anomaly in the three flavor linear sigma model