Accurate Estimates of 3D Ising Critical Exponents Using the Coherent-Anomaly Method

An analysis of the critical behavior of the three-dimensional Ising model using the coherent-anomaly method (CAM) is presented. Various sources of errors in CAM estimates of critical exponents are discussed, and an improved scheme for the CAM data analysis is tested. Using a set of mean-field type approximations based on the variational series expansion approach, accuracy comparable to the most precise conventional methods has been achieved. Our results for the critical exponents are given by $\alpha=\afin$, $\beta=\bfin$, $\gamma=\gfin$ and $\delta=\dfin$.