Cluster Algorithm Renormalization Group Method

TL;DR

This paper introduces a self-consistent cluster algorithm combined with Renormalization Group techniques to efficiently study critical phenomena, achieving high accuracy and faster computations for larger lattice sizes.

Contribution

It presents a novel method that integrates cluster algorithms with Renormalization Group on the lattice, improving speed and scalability over previous Monte Carlo approaches.

Findings

Accurately computes critical exponents $ u$ and $\eta$.

Demonstrates faster performance compared to standard methods.

Enables simulation of larger lattices within feasible computational times.

Abstract

We present a self consistent method based on cluster algorithms and Renormalization Group on the lattice to study critical systems numerically. We illustrate it by means of the 2D Ising model. We compute the critical exponents $\nu$ and $\eta$ and the renormalization group flow of the probability density function of the magnetization. The results, compared to the standard Monte Carlo Renormalization Group proposed by Swendsen [1], are very accurate and the method works faster by a factor which grows monotonically with the lattice size. This allows to simulate larger lattices in reachable computational times.