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

TL;DR

This paper models the evolution of collective emotions in online communities using a stochastic process, revealing a phase transition from mixed to ordered emotional states driven by preferential cluster growth.

Contribution

It introduces a one-dimensional stochastic model with long-range memory that captures the dynamical phase transition in online emotional discussions.

Findings

System exhibits a phase transition from mixed to ordered states.

Order emerges at a critical preference exponent value.

Numerical simulations agree with analytical predictions.

Abstract

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.