Dynamical replica analysis of processes on finitely connected random graphs II: Dynamics in the Griffiths phase of the diluted Ising ferromagnet

TL;DR

This paper extends dynamical replica theory to analyze the Glauber dynamics of Ising models on finitely connected random graphs, revealing slow dynamics and phase transitions within the Griffiths phase, supported by simulations.

Contribution

It generalizes a recent dynamical replica approach to include arbitrary degree distributions and applies it to diluted Bethe lattices, predicting new dynamical phenomena.

Findings

Slowing down of dynamics in the Griffiths phase

Identification of a dynamical transition at lower temperatures

Quantitative agreement with Monte Carlo simulations

Abstract

We study the Glauber dynamics of Ising spin models with random bonds, on finitely connected random graphs. We generalize a recent dynamical replica theory with which to predict the evolution of the joint spin-field distribution, to include random graphs with arbitrary degree distributions. The theory is applied to Ising ferromagnets on randomly diluted Bethe lattices, where we study the evolution of the magnetization and the internal energy. It predicts a prominent slowing down of the flow in the Griffiths phase, it suggests a further dynamical transition at lower temperatures within the Griffiths phase, and it is verified quantitatively by the results of Monte Carlo simulations.