Infinite-volume limit of reduced s-d model with antiferromagnetically coupled impurities

The thermodynamic limit of free energy per electron lim ƒ(HF(n, M), β) (with the number of electrons n, number of impurities M and volume ¦Λ¦ tending to infinity under the constraints n¦Λ¦−1 = d, n−1M = v) of the reduced s-d Hamiltonian HF(n, M) with antiferromagnetic Ising and Heisenberg interactions between M spin S impurities is examined. It is shown that lim ƒ(HF(n, M), β) = lim ƒ(hF(n, M), β), where hF(n, M) represents a system of n electrons decoupled from M impurities which undergoes a second-order phase transition at Tc, accompanied at T < Tc by antiparallel alignment of impurity spins and those of mobile electrons with momenta close to the Fermi surface.