Coevolution of Glauber-like Ising dynamics and topology

TL;DR

This paper investigates a coevolving system of Ising spins and network topology, revealing complex phase transitions and states with coexisting opposite spins organized in clusters, using both simulations and mean field analysis.

Contribution

It introduces a novel coevolution model combining Glauber-like dynamics with network rewiring, uncovering new phase behaviors not seen in traditional models.

Findings

Rich phase diagram with multiple phase transitions

Existence of states with coexisting opposite spins in the same component

Mean field estimates of phase diagram features

Abstract

We study the coevolution of a generalized Glauber dynamics for Ising spins, with tunable threshold, and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of the two parameters of the model, the threshold and the rewiring probability. The diagram displays phase transitions of different types: spin ordering, percolation, connectedness. At variance with traditional coevolution models, in which all spins of each connected component of the graph have equal value in the stationary state, we find that, for suitable choices of the parameters, the system may converge to a state in which spins of opposite sign coexist in the same component, organized in compact clusters of like-signed spins. Mean field calculations enable one to estimate some features of the phase diagram.