An iterative aproach to Ising lattice models: aproximate expressions for the sum of δ-functions investigated

A special expression for the sum of δ-functions implies a new graphical representation of thermodynamic quantities. The process consisting in the reduction in the number of points on an arbitrarily chosen reference spin in this graphical representation leads to the replacement of the basic formulae for thermodynamic quantities by an iterative scheme. Simple assumptions of the form of correlations in the surrounding of the reference spin during the iterative procedure allow to find equations for correlation functions. We are specially concerned with the influence of different approximate expressions for the sum of δ-functions on the coefficients in the resulting equations. It is observed that the dependences of these coefficients on a common parameter are similar in form but shifted from the exact plot. (author). 1 fig., 16 refs