Critical behavior in short-time dynamics is investigated by a Monte Carlo study for the random-bond Potts ferromagnet with a trinary distribution of quenched disorders on two-dimensional triangular lattices. The universal dynamic scaling is verified and applied to estimate the critical exponents θ, z and β/ν for several realizations of the trinary distribution. Our critical scaling analysis strongly indicates that the bond randomness influences the critical universality.

The symmetric two-layer Ising model (TLIM) is studied by the corner transfer matrix renormalization group method. The critical points and critical exponents are calculated. It is found that the TLIM belongs to the same universality class as the Ising model. The shift exponent is calculated to be 1.773, which is consistent with the theoretical prediction of 1.75 with 1.3% deviation.

With Monte Carlo simulations we investigate the nonequilibrium critical dynamic behavior of the two-dimensional random-bond Ising model. Based on the short-time dynamic scaling form, we estimate all the static and dynamic exponents from dynamic processes starting with both disordered and ordered states. Corrections to scaling are carefully considered.

The renormalisation group approach is applied to the study of the short-time critical behaviour of the d-dimensional Ginzburg-Landau model with long-range interaction of the form in momentum space. Firstly the system is quenched from a high temperature to the critical temperature and then relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws and the initial slip exponents and of the order parameter and the response function respectively, are calculated to the second order in .

In 1989 Janssen, Schaub and Schmittmann have shown that universality and scaling hold already in the early stage of the dynamical evolution of statistical systems, if the system, initially at a very high temperature, is suddenly quenched to the critical temperature and then released to the dynamic evolution according to model A. This allows for a measurement of all the static and dynamic critical exponents and even for the critical point already in the short-time regime, i.e., far from equilibrium. Since the correlation length is still small here, the simulations do not suffer from critical slowing down, a problem encountered in the usual measurements in equilibrium. The concept has been successfully applied to a variety of statistical systems. We will report about recent results for the fully frustrated XY model, where the short-lime approach is particularly efficient, since the standard cluster algorithm does not apply because of the frustration.

We suggest the existence of initial order mixing in the short-time evolution of the kinetic Ashkin–Teller model. The phenomenological short-time scaling laws are tested with numerical simulation.

Comprehensive Monte Carlo simulations of the short-time dynamic behaviour are reported for the three-dimensional Ising model at criticality. Besides the exponent of the critical initial increase and the dynamic exponent z, the static critical exponents and as well as the critical temperature are determined from the power-law scaling behaviour of observables at the beginning of the time evolution. States of very high temperature as well as of zero temperature are used as initial states for the simulations.

Short-time dynamic scaling behavior of the 3D ± J Ising spin glass is studied by Monte Carlo methods. Starting the replicas with independent initial configurations with a small pseudo-magnetization, the dynamic evolution of the overlap q(t) between two replicas is measured. The initial increase of the overlap q(t) is observed and the corresponding exponent θ′ is obtained. From the scaling relation λ= d/z-θ′, the dynamic exponent z is estimated.

The dynamic relaxation process for the (2 + 1)-dimensional SU(2) lattice gauge theory at critical temperature is investigated with Monte Carlo methods. The critical initial increase of the Polyakov loop is observed. The dynamic exponents theta and z as well as the static critical exponent beta/upsilon are determined from the power law behavior of the Polyakov loop, the autocorrelation, and the second moment at the early stage of the time evolution. The universal short-time scaling behavior of the dynamic system is confirmed. The values of the exponents show that the dynamic SU(2) lattice gauge theory is in the same dynamic universality class as the dynamic Ising model.

With Monte Carlo methods we investigate the dynamic relaxation of the fully frustrated XY model in two dimensions below or at the Kosterlitz-Thouless phase transition temperature. Special attention is drawn to the sublattice structure of the dynamic evolution. Short-time scaling behaviour is found and universality is confirmed. The critical exponent $\theta$ is measured for different temperature and with different algorithms.

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 T-c and all the dynamic and static critical exponents theta, z, beta, and v.

Using Monte Carlo methods, the short-time dynamic scaling behaviour of two-dimensional critical XY systems is investigated. Our results for the XY model show that there exists universal scaling behaviour already in the short-time regime, but the values of the dynamic exponent z differ for different initial conditions. For the fully frustrated XY model, power law scaling behaviour is also observed in the short-time regime. However, a violation of the standard scaling relation between the exponents is detected.

We present a dynamic Monte Carlo study of the spin-1/2 quantum XY model in two-dimensions at the Kosterlitz–Thouless phase transition temperature. The short-time dynamic scaling behaviour is found and the dynamical exponents θ, z and the static exponent η are determined.

We simulate the kinetic Ashkin-Teller model with both ordered and disordered initial states, evolving in contact with a heat-bath at the critical temperature. The power law scaling behaviour for the magnetic order and electric order are observed in the early time stage. The values of the critical exponent θ vary along the critical line. Another dynamical exponent z is also obtained in the process.

The scaling behaviour of the persistence probability in the critical dynamics is investigated with both the heat-bath and the Metropolis algorithm for the two-dimensional Ising model and Potts model. Special attention is given to the dependence on the initial magnetization. The global persistence exponent is measured. Universality is confirmed.

We have numerically confirmed the universal short-time scaling behaviour of the critical dynamics for the two dimensional Potts model. Critical initial increase of the magnetization is observed and the new dynamic exponent θ is determined. Based on the scaling relation in the short-time dynamics, new ways for the determination of the critical point and all the static exponents as well as the dynamic exponent z have been proposed.

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 is directly determined. The results show that the exponent 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.

Recent investigation on the short-time dynamic scaling of critical dynamics is reviewed, with the aim of applying it to the field theory. The contents of this paper are as follows: (1) Short-time behavior of the critical relaxation dynamics, (2) Numerical evidence of the short-time scaling—2-dimensional Ising model and Universality, (3) Theoretical background of the generalized scaling form, (4) Application to a field theoretical model—(2+1)-dimensional SU(2) lattice gauge theory at finite temperature, and (5) Concluding remarks.

The short-time scaling behaviour of the critical dynamics for the two-dimensional Ising model and Potts model are investigated with both the heat-bath and the Metropolis algorithm. Special attention is drawn to universality. We observed that the microscopic time scale tmic after which the universal scaling behaviour appears is not always negligibly small. Taking carefully the effect of tmic into account, the critical exponents are extracted from the power law behaviour of the observables in the beginning of the time evolution. All the results are consistent and therefore universality and scaling are confirmed.