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.

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 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.

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.