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

TL;DR

This paper improves Monte Carlo renormalization for the 3D Ising model by optimizing blocking rules and including extended interactions, resulting in faster convergence and highly accurate critical exponents.

Contribution

It introduces an optimized Kadanoff blocking scheme with extended interactions, enhancing the analyticity and convergence of Monte Carlo renormalization for the 3D Ising model.

Findings

Critical exponents y_H=2.481(1) and y_T=1.585(3) were obtained.

The method shows fast convergence and high accuracy.

Inclusion of second and third neighbor interactions reduces scaling corrections.

Abstract

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 Ising model with reduced corrections to scaling. This is achieved by including interactions with second and third neighbors. As a consequence of the improved analyticity properties, this Monte Carlo renormalization method yields a fast convergence and a high accuracy. The results for the critical exponents are y_H=2.481(1) and y_T=1.585(3).