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

Abstract

An expression for the chain length probability distribution p(l) of a one dimensional Ising chain was derived using the cluster variation method formalism, the p(l) 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 (x) planes of the YBa(2)Cu(3)O(6+x) type high-T (c) superconducting materials. Equivalency between ASYNNNI and 1d Ising model is discussed.