A detailed and qualitative matrix representation of the one-dimensional periodic Anderson model (PAM) is presented giving the ground state as a function of band filling using the exact diagonalization technique.The simplest lattice system of two electrons on two sites is consider, in the study the results of the matrix element were compared and it was found that for the symmetric case where the energy of the f electrons Ef =-U/2 and the hybridization matrix element V switched off, the results are consistent with the Kondo model Hamiltonian matrix in the J =0 region.The results obtained in the study are also in agreement with the famous Hubbard (t –u) model if the Hybridization term V of the PAM and the energy of the localized f orbital Ef are switched off. The results of the ground state energies were used to determine the transition from antiferromagnetic (AFM) phase to a ferromagnetic (FM) phase and vice versa.
Keywords: Anderson model, Antiferromagnetism, Ferromagnetism, transition point
