Dynamical phase transition due to preferential cluster growth of collective emotions in online communities

We consider a preferential cluster growth in a one-dimensional stochastic model describing the dynamics of a binary chain with long-range memory. The model is driven by data corresponding to emotional patterns observed during online communities’ discussions. The system undergoes a dynamical phase transition. For low values of the preference exponent, both states are observed during the string evolution in the majority of simulated discussion threads. When the exponent crosses a critical value, in the majority of threads an ordered phase emerges, i.e. from a certain time moment only one state is represented. The transition becomes discontinuous in the thermodynamical limit when the discussions are infinitely long and even an infinitely small preference exponent leads to the ordering behavior in every discussion thread. Numerical simulations are in a good agreement with approximated analytical formula.

💡 Research Summary

The paper investigates how emotional expressions evolve in online discussion threads by introducing a minimalist stochastic model that captures the preferential growth of same‑emotion clusters. Real‑world data from forums and social media show that once a sequence of identical emotional posts (a “cluster”) becomes long, the likelihood that the next post continues the same emotion increases. To formalize this, the authors represent a discussion as a one‑dimensional binary chain where each site is either positive (+) or negative (–). Starting from a random initial state, the probability that the next token repeats the current emotion is defined as

\