Phase-ordering kinetics on graphs

TL;DR

This paper investigates the phase-ordering kinetics of the Ising model on various complex graphs, revealing universal dynamical exponents and their relation to network topology.

Contribution

It introduces a numerical study of phase-ordering on fractal and random graphs, highlighting the temperature-independent response exponent and its topological significance.

Findings

The response exponent $a_\chi$ is universal across different temperatures and pinning conditions.

Scaling properties and dynamical exponents are characterized for each graph structure.

A relation between $a_\chi$ and network topology is proposed.

Abstract

We study numerically the phase-ordering kinetics following a temperature quench of the Ising model with single spin flip dynamics on a class of graphs, including geometrical fractals and random fractals, such as the percolation cluster. For each structure we discuss the scaling properties and compute the dynamical exponents. We show that the exponent $a_\chi$ for the integrated response function, at variance with all the other exponents, is independent on temperature and on the presence of pinning. This universal character suggests a strict relation between $a_\chi$ and the topological properties of the networks, in analogy to what observed on regular lattices.