Dynamical real-space renormalization group calculations with a new clustering scheme on random networks

TL;DR

This paper introduces a new clustering scheme for real-space renormalization group calculations on random networks, improving accuracy in high dimensions and providing results consistent with Monte Carlo simulations.

Contribution

A novel clustering scheme that preserves network connectivity, enhancing the accuracy of dynamical critical exponents in high-dimensional systems.

Findings

Accurate dynamical critical exponents for the kinetic Ising model in 2D and 3D.

Improved phase diagram analysis for bond-diluted lattices.

Exact critical exponents on hierarchical lattices with power-law degree distributions.

Abstract

We have defined a new type of clustering scheme preserving the connectivity of the nodes in network ignored by the conventional Migdal-Kadanoff bond moving process. Our new clustering scheme performs much better for correlation length and dynamical critical exponents in high dimensions, where the conventional Migdal-Kadanoff bond moving scheme breaks down. In two and three dimensions we find the dynamical critical exponents for the kinetic Ising Model to be z=2.13 and z=2.09, respectively at pure Ising fixed point. These values are in very good agreement with recent Monte Carlo results. We investigate the phase diagram and the critical behaviour for randomly bond diluted lattices in d=2 and 3, in the light of this new transformation. We also provide exact correlation exponent and dynamical critical exponent values on hierarchical lattices with power-law degree distributions, both in the pure and random cases.