The long-range correlations of various Ising lattices
The object of this paper is to determine the long-range order parameter for any Ising lattice whose partition function can be evaluated by existing methods. The partition function of a general class of two-dimensional lattices is evaluated by a technique found byGreek andHurst, and this technique is extended to determine correlation coefficients. In this way the determination of the long-range correlation coefficients is reduced to an eigenvalue problem, which can be solved by algebraic methods. A simple formula is found for the long-range order parameter, which contains, but is considerably more general than the known result for the rectangular lattice.