Phase transition and opinion–action decoupling in social innovation: A two-layer network model with the spiral of silence

Complex social systems often exhibit a divergence between public opinions and actions. This decoupling arises because the exposed actions within a group represent a biased subset of true behaviors. To uncover the micro-macro mechanisms behind opinion–action gap, we develop a co-evolutionary model from a computational statistical physics perspective, grounded in a two-layer coupled network. Our framework integrates opinion dynamics, decision-making, and the spiral of silence theory, creating a feedback loop between opinion layer and action layer. Individuals update their opinions based on both neighbor opinions and the observable actions of others, while their decision to expose an action depends on the perceived local majority, a mechanism aligned with the spiral of silence. Simulations reveal that our model can capture essential dynamics of social innovation diffusion: (1) The emergence of innovation is controllable via leader proportion (local field) or media influence (global field). (2) The feedback from actions to opinions can inhibit change; excessively strong coupling creates a negative feedback trap. (3) Under specific condition, such as leaders whose “words differ from deeds”, the system stabilizes in a macroscopic symmetry-broken non-popular norm. In this state, group opinion favor innovation while exposed action oppose it, demonstrating systematic bias in collective cognition. This work provides a computational statistical physics framework for analyzing the emergent transition of social norms and the diffusion of collective innovation.