Hysteresis in the zero-temperature random field Ising model on directed random graphs

TL;DR

This paper investigates hysteresis phenomena in the zero-temperature random-field Ising model on directed random graphs, revealing how connectivity influences critical behavior and implications for opinion dynamics.

Contribution

It provides the first analytical solution for the model on directed graphs and explores the impact of external influence on phase transitions in opinion dynamics.

Findings

Critical behavior varies with connectivity $z$ on directed graphs.

Analytic solution supports numerical results.

External influence can induce first-order phase transitions.

Abstract

We use zero-temperature Glauber dynamics to study hysteresis in the random-field Ising model on directed random graphs. The critical behavior of the model depends on the connectivity $z$ of the graph rather differently from that on undirected graphs. Directed graphs and zero-temperature dynamics are relevant to a wide class of social phenomena including opinion dynamics. We discuss the efficacy of increasing external influence in inducing a first-order phase transition in opinion dynamics. The numerical results are supported by an analytic solution of the model.