Peer influence breaks ergodicity in an opinion dynamics model with external information

Abstract We present a stochastic imitation-based model of opinion dynamics in which agents balance social conformity with responsiveness to an external signal. The model captures how populations evolve between two binary opinion states, driven by peer influence and noisy external information. Through both memory-less and memory-based implementations, we identify a critical threshold of social sensitivity that separates an ergodic phase—where agents collectively track the external signal—from a non-ergodic phase characterised by persistent consensus and reduced adaptability to external changes. Analytical results and simulations reveal that memory in decision-making smooths the transition and lowers the critical threshold for ergodicity breaking. Extending the model to various network structures confirms the robustness of the observed phase transition. We further discuss empirical methodologies for estimating the critical threshold and show how the model may be applied to real-world domains. Our findings contribute to understanding how social conformity, memory effects and randomness jointly shape collective behaviour, with implications for predicting social tipping points and influencing large-scale social dynamics.