Multifractal and Phase Transition for Bi-Dimensional Brownian Motion

In this paper, we have studied the multifractal characterstics of bi-dimensional Brownian motion by Brownian dynamics simulation. The existence of a phase transition associated with a breakdown in the scaling at a critical value of q in the multifractal spectrum. is deduced. The multifractality is reduced by increasing the number of steps of the Brownian trajectories, tending to disappear for an infinitely long trajectory.