Dynamical Decimation Renormalization-Group Technique: Kinetic Gaussian Model on Non-Branching, Braching and Multi-branching Koch Curve

TL;DR

This paper introduces a generalized dynamical real-space renormalization method for spin systems and applies it to analyze the critical slowing down of Gaussian spin models on various Koch curve fractals, revealing a universal critical exponent.

Contribution

It proposes a new decimation renormalization technique based on single-spin transition dynamics and applies it to fractal lattices to compute critical exponents.

Findings

Calculated dynamical critical exponent z for different Koch curves.

Discovered a universal relation z=1/nu across fractal lattices.

Validated the method's effectiveness for complex fractal geometries.

Abstract

A generalizing formulation of dynamical real-space renormalization that suits for arbitrary spin systems is suggested. The new version replaces the single-spin flipping Glauber dynamics with the single-spin transition dynamics. As an application, in this paper we mainly investigate the critical slowing down of the Gaussian spin model on three fractal lattices, including nonbranching, branching and multibranching Koch Curve. The dynamical critical exponent $z$ is calculated for these lattices using an exact decimation renormalization transformation in the assumption of the magnetic-like perturbation, and a universal result $z=1/\nu $ is found.