Phase ordering in disordered and inhomogeneous systems

TL;DR

This paper investigates the coarsening dynamics of the Ising model on disordered and fractal substrates, proposing a unified interpretation based on two classes of growth-laws linked to topological features.

Contribution

It introduces a unifying framework for phase-ordering dynamics in disordered systems, connecting growth-laws to topological properties and phase transition presence.

Findings

Identification of two dynamical classes: logarithmic and power-law growth.

Correlation between topological features and the type of growth-law.

Insight into how disorder affects phase-ordering processes.

Abstract

We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of dynamical behaviors characterized by different growth-laws of the ordered domains size - logarithmic or power-law respectively. It is conjectured that the interplay between these dynamical classes is regulated by the same topological feature which governs the presence or the absence of a finite-temperature phase-transition.