Monte Carlo renormalization group calculation for the d=3 Ising Model using a modified transformation

TL;DR

This paper introduces a modified Monte Carlo renormalization group method with a tunable parameter to accurately determine critical properties of the 3D Ising model without prior critical temperature knowledge.

Contribution

It presents a new iterative approach using a modified block-spin transformation that improves convergence and allows simultaneous calculation of critical temperature and exponents.

Findings

Accurate critical temperature and exponents obtained without prior knowledge.

Modified transformation enhances convergence in Monte Carlo renormalization.

Method applicable to high-accuracy critical property calculations.

Abstract

We present a simple approach to high-accuracy calculations of critical properties for the three-dimensional Ising model, without prior knowledge of the critical temperature. The iterative method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group trajectory. We found experimentally that the iterative method enables the calculation of the critical temperature simultaneously with a critical exponent.