Calculation of the zero-field susceptibility and critical temperature of Ising magnets on the basis of the principle of limit similarity

A simple analytical approximate method for the calculation of the zero-field susceptibility and the critical temperature for the Ising model is proposed. The analysis is based on the rule of limit correspondence. Assuming that the first three terms of the high-temperature series expansion are known, accurate values for the eight types of lattices are obtained. These values (excepting the honeycomb lattice) differ from those obtained through series extrapolation by 0.8% rms, and generally compare favorably to estimates computed through the heuristic Bishop formula. In connection with an associated percolation problem, a more accurate formula for the critical bond percolation probability is proposed. © 1993 The American Physical Society.