Numerical evaluations of the critical properties of the two - dimensional Ising modeP

Scaling transformations are used in numerical calculations of the properties of the two4imensional Ising model near its critical point. When compared with the exact Onsager solution, the best approximation is seen to lead to 1 part in 10 accuracy for the two largest scaling indices. This rather accurate calculation is obtained by utilizing a scaling transformation which depends upon a parameter. The parameter is set by demanding that two different evaluations of the magnetic eigenvalue agree with one another. One evaluation is found via the standard eigenvalue method; the other comes from a consistency condition for the spin-spin correlation function. This condition may also be used to distinguish scaling eigenvalues from other eigenvalues.