Chain length probability distribution — equivalence of ASYNNNI and 1d Ising model

Abstract

Abstract:An expression for the chain length probability distribution ( ) of a one dimensional Ising chain was derived using the cluster variation method formalism, the ( ) being expressed through the pair cluster probabilities. It was shown numerically that the same expression also applies in the case of one dimensional chains formed along one of the next-nearest neighbor interactions included in the two dimensional ASYNNNI (Asymmetric Next-Nearest Neighbor Ising) model, widely used to describe the statistics of oxygen ordering in the basal CuO planes of the YBa 2 Cu 3 O 6+ type high-T superconducting materials. Equivalency between ASYNNNI and 1d Ising model is discussed.