Monte Carlo Renormalization of the 3D Ising Model: Analyticity and Convergence

We review the assumptions on which the Monte Carlo renormalization technique is based, in particular, the analyticity of the block-spin transformations. On this basis, we select an optimized Kadanoff blocking rule in combination with the simulation of a $d=3\mathrm{}$ Ising model with reduced corrections to scaling. This is achieved by including interactions with second and third neighbors. As a consequence of the improved transformation, this Monte Carlo renormalization method yields a fast convergence and a high accuracy. The results for the critical exponents are $y_H=2.481\mathrm{}\left(1\right)$ and $y_T=1.585\mathrm{}\left(3\right)$.