Multi-step relaxations in Glauber dynamics of a bond-diluted Ising model on a Bethe lattice

TL;DR

This paper studies the Glauber dynamics of a bond-diluted Ising model on a Bethe lattice, revealing multi-step relaxation phenomena at intermediate times in the Griffiths phase, supported by an approximate theory and Monte Carlo simulations.

Contribution

It introduces an approximate theoretical framework that accurately describes the dynamics of a bond-diluted Ising model on a Bethe lattice, highlighting multi-step relaxations in the Griffiths phase.

Findings

Good agreement between theory and Monte Carlo simulations.

Identification of multi-step relaxation phenomena in the Griffiths phase.

Exact results for equilibrium properties of the model.

Abstract

Glauber dynamics of a bond-diluted Ising model on a Bethe lattice (a random graph with fixed connectivity) is investigated by an approximate theory which provides exact results for equilibrium properties. The time-dependent solutions of the dynamical system derived by this method are in good agreement with the results obtained by Monte Carlo simulations in almost all situations. Furthermore, the derived dynamical system exhibits a remarkable phenomenon that the magnetization shows multi-step relaxations at intermediate time scales in a low-temperature part of the Griffiths phase without bond percolation clusters.