A unified multiscale framework for phase transitions in opinion dynamics: integrating interaction mechanisms, establishing an empirical phase criterion, and predicting cluster structures

Abstract Public discussions on digital platforms often evolve toward different end states, including convergence, polarisation, and the coexistence of multiple camps, even under similar levels of controversy. Existing research on opinion dynamics has examined interaction mechanisms, phase-transition boundaries, steady-state structures, and multistability largely in separate strands. This study proposes and tests a unified multiscale framework that integrates these elements within a single agent-based continuous-opinion model. The framework is built on a dual-threshold mechanism combining assimilation, repulsion, and non-interaction. From the initial distribution of neighbourhood opinion differences, an empirical phase criterion is constructed whose sign indicates whether contraction or expansion and decoupling dominate. A four-coefficient empirical prediction formula is further introduced to estimate the steady-state cluster number under polarised conditions, together with a multistability correction term based on repeated-run statistics. Systematic simulations generate outcomes ranging from consensus and bipolar polarisation to multi-cluster coexistence. Across the baseline parameter grid, the empirical phase criterion achieves 86.7% phase-sign agreement with simulated end states, while the cluster-number prediction is within one cluster of the observed modal value in 82.26% of analysable conditions. Additional analyses show that stochasticity, initial conditions, finite-size effects, and competition among basins of attraction can alter the realised steady-state structure. Phase transition is used here in an operational structural sense, referring to a reproducible change in steady-state opinion structure across a narrow threshold interval rather than a thermodynamic transition. Because all evidence is generated within the same agent-based model, the framework should be interpreted as a simulation-calibrated empirical account whose broader validity requires further testing across alternative empirical and network settings.