Quantitative Investigation of Network Externalities Based on Extended Ising Model

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As examples with strong effect of network externality, we studied the growth of the mobile phone market in 1990's and recent facebook. It was found that the number of the users grow exponentially if it is less than 20% of all the possible users. It moves to linear growth if it is above 20%.We investigated if it is possible to explain these phenomena based on Ising model. It was found that the growth curve obtained by numerical calculation shows a qualitative change from exponential growth to linear one at the threshold of 20%. Although there are two parameters within the model, it was found that they give the time scale to reach 20% but do not change the threshold of 20%.