Statistical mechanics of coevolving spin system

TL;DR

This paper introduces a statistical mechanics framework for a coevolving spin system on an adaptive network, revealing complex phase behaviors driven by the interplay of node states and network topology.

Contribution

It combines the Ising model with correlated random network theory to analyze the coupled dynamics of spins and network structure, providing new insights into their joint phase transitions.

Findings

Rich phase diagrams with multiple phase transitions

Coupling between spin states and network topology is essential

Complex behavior observed in coevolving systems

Abstract

We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a Hamiltonian that merges the classical Ising model and the statistical theory of correlated random networks. As a result, we obtain rich phase diagrams with different phase transitions both in the state of nodes and in the graph topology. We argue that the coupling between the spin dynamics and the structure of the network is crucial in understanding the complex behavior of real-world systems and omitting one of the approaches renders the description incomplete.