Phase transition of dynamical herd behaviors for Yen-Dollar exchange rates

We study the herd behavior and the phase transition for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution of returns satisfies the power-law behavior P(R)≃R-β with scaling exponents β=3.11, 2.81, and 2.29 at time intervals τ=1min, 30min, and 1 h. The crash region in which the probability density increases with the increasing return appears, when the herding parameter h satisfies h⩾2.33 for the case of τ<30min. We especially obtain that no crash occurs τ>30min and that the probability distribution of price returns occurs in the phase transition at τ=30min.