Metastable opinion dynamics with hidden preferences: an Ising model with neutral agents

TL;DR

This paper introduces a new Ising-type model for opinion dynamics that separates private preferences from public opinions, incorporating neutral agents, and analyzes metastability and transition times using geometric and probabilistic methods.

Contribution

It extends classical Ising models by explicitly modeling hidden preferences and neutrality, providing a detailed metastability analysis with new isoperimetric inequalities for polyominoes.

Findings

Characterization of stable and metastable opinion configurations

Identification of energy barriers and stability levels

Asymptotic estimates for transition and mixing times

Abstract

We introduce a new Ising-type framework for opinion dynamics that explicitly separates private preferences from publicly expressed binary opinions and naturally incorporates neutral agents. Each individual is endowed with an immutable hidden preference, while public opinions evolve through Metropolis dynamics on a finite graph. This formulation extends classical sociophysical Ising models by capturing the tension between internal conviction, social conformity, and neutrality. Focusing on highly symmetric grid networks and spatially structured hidden-preference patterns, we analyze the resulting low-temperature dynamics using the pathwise approach to metastability. We provide a complete characterization of stable and metastable configurations, identify the maximal stability level of the energy landscape, and derive sharp asymptotics for hitting and mixing times. A central technical contribution is a new family of isoperimetric inequalities for polyominoes on the torus, which emerge from a geometric representation of opinion clusters and play a key role in determining critical configurations and energy barriers. Our results provide a quantitative understanding of how spatial heterogeneity in hidden preferences qualitatively reshapes collective opinion transitions and illustrate the power of geometric and probabilistic methods in the study of complex interacting systems.