Strong-coupling limit in dilute alloys

Abstract

We obtain the energy spectrum and calculate the partition function for Zener's s-d exchange-interaction model in the strong-coupling limit and with constant interaction-JN between impurity ions and conduction electrons. The system is shown to undergo a transition to an ordered state independently of the sign of J and for arbitrarily small impurity concentration c. The critical temperature Tc is given by 8kTc=J(2c)12 for ferromagnetic coupling (J>0) and by 8kTc=|J|[1-(1-2c)12] for antiferromagnetic coupling (J12 and J<0 our procedure for evaluating the statistical sum becomes invalid. © 1966 The American Physical Society.