Julian Sienkiewicz, Janusz A. Hołyst
We introduce a one-dimensional model basing on a special kind of asymmetrical one-side Ising-like dynamics. The model is equipped with the growth feature by adding a new node to the chain in each time-step. A spin of every succeeding node is influenced by the previous one but not vice-versa (the system in not hamiltonian). Owing to model's simplicity (it is an equivalent to a Markov chain) we are able exactly solve it in the presence of external field h. We conceive it as suitable for modeling for emotional online discussions arranged in a chronological order, where spin in every node conveys emotional valence of a subsequent post. We study the dependence of the chain's average spin on external influence h (community tendency toward a selected valence) and noise level T (uncertainty of the emotional behavior). This leads us to an observation of three distinct phases - the first, where discussion evolution is determined by its launching message only, the second, in which the mostly observed emotion is coping the external influence, a finally, the third one, where the outcome is subject to fluctuations.
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http://arxiv.org/abs/1303.2079
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