Based on the scaling relation for the dynamics at the early time, a new method is proposed tc measure both the static and dynamic critical exponents. The method is applied to the two-dimensional Ising model. The results are in good agreement with the existing results. Since the measurement is carried out in the initial stage of the relaxation process starting from independent initial configurations. our method is efficient.

The recently discovered two-phase phenomenon in financial markets [Nature 421, 130 (2003)] is examined with the German financial index DAX, minority games, and dynamic herding models. It is observed that the two-phase phenomenon is an important characteristic of financial dynamics, independent of volatility clustering. An interacting herding model correctly produces the two-phase phenomenon.

We numerically solve microscopic deterministic equations of motion for the two-dimensional f4 theory with random initial states. Phase ordering dynamics is investigated. Dynamic scaling is found and it is dominated by a fixed point corresponding to the minimum energy of random initial states.

Taking the two-dimensional f4 theory, we numerically solve the deterministic equations of motion with random initial states. Short-time behavior of the solutions is systematically investigated. Assuming that the solutions generate a microcanonical ensemble of the system, we demonstrate that the secondorder phase transition point can be determined from the short-time dynamic behavior. An initial increase in the magnetization and a critical slowing down are observed. The dynamic critical exponent z, the new exponent u, and the static exponents b and n are estimated. The deterministic dynamics with random initial states is in the same universality class as the Monte Carlo dynamics.