Effect of initial conditions on Glauber dynamics in complex networks

TL;DR

This paper explores how initial spin configurations, based on centrality measures, influence zero-temperature Glauber dynamics in complex networks, revealing critical points and non-trivial behaviors that depend heavily on initial conditions.

Contribution

It demonstrates that initial conditions significantly affect Glauber spin dynamics in complex networks, comparable to the influence of network structure itself.

Findings

Initial spin configurations lead to diverse diffusive behaviors.

Presence of critical points in the relationship between initial and final spin states.

Initial majority spins are not always retained in the final state.

Abstract

The effect of initial spin configurations on zero-temperature Glauber spin dynamics in complex networks is investigated. In a system in which the initial spins are defined by centrality measures at the vertices of a network, a variety of non-trivial diffusive behaviors arise, particularly in relation to functional relationships between the initial and final fractions of positive spins, some of which exhibit a critical point. Notably, the majority spin in the initial state is not always dominant in the final state, and the phenomena that occur as a result of the dynamics differ according on the initial condition, even for the same network. It is thus concluded that the initial condition of a complex network exerts an influence on spin dynamics that is equally as strong as that exerted by the network structure.