Numerically we simulate the short-time behaviour of the critical dynamics for the two dimensional Ising model and Potts model with an initial state of very high temperature and small magnetization. Critical initial increase of the magnetization is observed. The new dynamic critical exponent θ as well as the exponents z and 2β/ν are determined from the power law behaviour of the magnetization, auto-correlation and the second moment. Furthermore the calculation has been carried out with both Heat-bath and Metropolis algorithms. All the results are consistent and therefore universality and scaling are confirmed.

Dynamic relaxation of the XY model quenched from a high temperature state to the critical temperature or below is investigated with Monte Carlo methods. When a non-zero initial magnetization is given, in the short-time regime of the dynamic evolution the critical initial increase of the magnetization is observed. The dynamic exponent θ is directly determined. The results show that the exponent θ varies with respect to the temperature. Furthermore, it is demonstrated that this initial increase of the magnetization is universal, i.e. independent of the microscopic details of the initial configurations and the algorithms.

No abstract

No abstract

No abstract