Zero temperature Glauber dynamics on complex networks

TL;DR

This paper investigates zero-temperature Glauber dynamics on complex networks with power-law degree distributions, revealing discrepancies between mean-field theory predictions and numerical simulations regarding the time to reach full order.

Contribution

It challenges the mean-field theory predictions for Glauber dynamics on complex networks, showing the need for more accurate models.

Findings

Mean time to order is finite or logarithmically divergent, depending on degree distribution exponent.

Numerical simulations contradict mean-field theory, indicating its inadequacy.

Mean-field assumptions do not accurately describe the dynamics on complex networks.

Abstract

We study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power-law degreedistribution. Application of mean-field theory yields as main prediction that for symmetric disordered initial conditions the mean time to reach full order is finite or diverges as a logarithm of the system size N, depending on the exponent of the degree distribution. Extensive numerical simulations contradict these results and clearly show that the mean-field assumption is not appropriate to describe this problem.