Based on the short-time dynamic scaling form, a dynamic approach is proposed to numerically tackle the Kosterlitz-Thouless phase transition. Taking the two-dimensional XY model as an example, the exponential divergence of the spatial correlation length, the transition temperature TKT, and all critical exponents are computed. Compared with Monte Carlo simulations in equilibrium, we obtain data at temperatures closer to TKT.

The dynamic relaxation process for the two dimensional Potts model at criticality starting from an initial state with very high temperature and arbitrary magnetization is investigated with Monte Carlo methods. The results show that there exists universal scaling behavior even in the short-time regime of the dynamic evolution. In order to describe the dependence of the scaling behavior on the initial magnetization, a critical characteristic function is introduced.

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.

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.

Using Monte Carlo simulations, we systematically investigate the nonequilibrium dynamics of the chiral degree of freedom in the two-dimensional fully frustrated XY model. By means of the short-time dynamics approach, we estimate the second order phase transition temperature Tc and all the dynamic and static critical exponents u, z, b, and n. [S0031-9007(98)06479-5]

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.

The probability distribution function of magnetization of critical magnetic systems is investigated with Monte Carlo simulations. Its generic features beyond the standard universality are revealed. A mean field ansatz explains the phenomena partly.

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.