We consider a   preferential cluster growth in a  stochastic  model describing the dynamics of a binary  Markov chain with an additional  long-range memory. The model is driven by data describing  emotional patterns observed in online community discussions with binary states corresponding to emotional valencies. Numerical simulations and approximate analytical calculations show that the pattern of  frequencies depends on a preference exponent related to  the memory strength in our model.   For low values of this exponent in the majority of simulated discussion threads both emotions are observed with similar frequencies.  When the exponent increases  an ordered  phase emerges in the majority of threads, i.e.  only one emotion is represented from a certain  moment.   Similar changes are observed with increase of  a single-step Markov memory value. The transition becomes discontinuous in the thermodynamical limit when  discussions are infinitely long and even an infinitely small preference exponent leads to  ordered behavior in each discussion thread.  Numerical simulations are in a good agreement with approximated analytical formula. The model resembles a dynamical phase transition observed in other Markov models with a long memory where  persistent dynamics follows from a transition to a superdiffusion phase. The ordered patterns  predicted  by our model have been found in Blog06 dataset  although their number   is limited by fluctuations and sentiment classification errors.

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