Coherent Anomaly Method in Critical Phenomena. II. Applications to the Two- and Three-Dimensional Ising Models

A systematic procedure of constructing a series of cluster-mean-field approximations is established to investigate the coherent anomalies of the mean-field critical coefficients χ( L , T c ( L )) in the two- and three-dimensional Ising models. The values of critical exponents as well as the critical temperatures are estimated by means of the new method (Coherent Anomaly Method) as T c * =2.230(0.038) J / k B , γ=1.785(0.116) for the two-dimensional square lattice and T c * =4.529(0.058) J / k B , γ=1.258(0.068) for the three-dimensional simple cubic lattice. The results suggest that the present approach to study critical phenomena is very promising.