Before revision:  Here we give empirical evidence, by making as few assumptions as possible, that the market microstructure capturing almost all of the available information in the data of stock markets does not involve higher order than pairwise interactions. We give an economic interpretation of this pairwise model. We show that it accurately recovers the empirical correlation coefficients thus the collective behaviors are quantitatively described by models that capture the observed pairwise correlations but no higher-order interactions. Furthermore, we show that an order-disorder transition occurs as predicted by the pairwise model.
After revision:  Here , we show that an order-disorder transition occurs as predicted by the pairwise model.