arXiv subjects
Publications and source records attributed to B. Zheng.
We present a dynamic Monte Carlo study of the Kosterlitz-Thouless phase transition for the spin-1/2 quantum XY model in two dimensions. The short-time dynamic scaling behaviour is found and the dynamical exponent $θ$, $z$ and the static exponent $η$ are determined at the transition temperature.
Using Monte Carlo simulations, we systematically investigate the non-equilibrium dynamics of the chiral degree of freedom in the two-dimensional fully frustrated XY model. The critical initial increase of the staggered chiral magnetization is observed. 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 $θ$, z, $β$ and $ν$.
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 drawn to the dependence on the initial magnetization. The global persistence exponent is measured. Universality is confirmed.
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.
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.
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 $θ$ and $z$ as well as the static critical exponent $β/ν$ are determined from the power law behaviour of the Polyakov loop, the auto-correlation and the second moment at the early stage of the time evolution. The results are well consistent and universal short-time scaling behaviour 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 $θ$ is measured for different temperature and with different algorithms.
The short-time behaviour of the critical dynamics for magnetic systems is investigated with Monte Carlo methods. Without losing the generality, we consider the relaxation process for the two dimensional Ising and Potts model starting from an initial state with very high temperature and arbitrary magnetization. We confirm the generalized scaling form and observe that the critical characteristic functions of the initial magnetization for the Ising and the Potts model are quite different.
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 behaviour even in the short-time regime of the dynamic evolution. In order to describe the dependence of the scaling behaviour on the initial magnetization, a critical characteristic function is introduced.
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.
The dynamic process for the two dimensional three state Potts model in the critical domain is simulated by the Monte Carlo method. It is shown that the critical point can rigorously be located from the universal short-time behaviour. This makes it possible to investigate critical dynamics independently of the equilibrium state. From the power law behaviour of the magnetization the exponents $β/ (νz)$ and $1/ (νz)$ are determined.
We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a new method to measure both the dynamic and static critical exponents are reported, based on the finite size scaling for the dynamics at the early time. From the time-dependent Binder cumulant, the dynamical exponent $z$ is extracted independently, while the static exponents $β/ν$ and $ν$ are obtained from the time evolution of the magnetization and its higher moments.
The universal behaviour of the short-time dynamics of the three state Potts model in two dimensions at criticality is investigated with Monte Carlo methods. The initial increase of the order is observed. The new dynamic exponent $θ$ as well as exponent $z$ and $β/ν$ are determined. The measurements are carried out in the very beginning of the time evolution. The spatial correlation length is found to be very short compared with the lattice size.
Based on the scaling relation for the dynamics at the early time, a new method is proposed to 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 time evolution of the three-dimensional critical Ising model relaxing from a nonequilibrium initial state is studied by means of Monte Carlo simulation. We observe the characteristic initial increase of the (spatially) averaged magnetization predicted by Janssen et al. The exponent theta' that governs the initial behavior is determined, and the dependence of the long-time linear decay on the initial magnetization analyzed. Our simulation corroborates earlier results derived from continuum models.
A generalized gauge invariant Ising model on random surfaces with non-trivial topology is proposed and investigated with the dual transformation. It is proved that the model is self-dual in case of a self-dual lattice. In special cases the model reduces to the known solvable Ising-type models.
In the numerical simulation of certain field theoretical models, the complex Langevin simulation has been believed to fail due to the violation of ergodicity. We give a detailed analysis of this problem based on a toy model with one degree of freedom ($S=-β\cosθ$). We find that the failure is not due to the defect of complex Langevin simulation itself, but rather to the way how one treats the singularity appearing in the drift force. An effective algorithm is proposed by which one can simulate the ${1/β}$ behaviour of the expectation value $<\cosθ>$ in the small $β$ limit.