  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.
