Monte Carlo Study Of Zero-temperature Dynamics For Ising System

Using Monte Carlo method,we investigate the dynamical evolution of two-dimensional Ising system quenched from high temperature to zero temperature.The main results of this thesis are as follows:1.The effect of initial configuration of the Ising system on its dynamical evolution is investigated.If the magnetization in the initial configuration equals to zero(in this case the number of up spins is equal to that of down spins),the final state is symmetric.For example, the magnetization is symmetric about zero and the ratio of up-spin ground state is the same with down-spin ground state or stripe state.If the magnetization in the initial configuration not equal to zero,the symmetry will'disappear.2.The anomalous behavior in long-time dynamical evolution is studied.At the long-time stage of the dynamical evolution,there is a very long relaxation which causing some anomalous behaviors.For example,the power-law decay in energy and persistence will be broken.By studying-the fluctuations of magnetization and energy in the anomalous dynamics,we find that the energy is steady and can be used to character the anomalous behavior,but the magnetization always fluctuates,thus it can not be used to character the anomalous behavior.In addition,we find that when anomalous behavior appears the energy is 4/L and slightly larger than 2/L in ground state realization and the stripe state realization,respectively,where L is the lattice size.3.By studying the constructions of the ground state and stripe state,we find the sources of anomalous dynamical evolution.In ground state realization,the anomaly originated from the diagonal stripe configuration,and in stripe state realization,the anomaly comes from the sawtooth-like configuration which appears in the last stage of evolution.The energy values of the special configurations are in good accordance with those in simulation.4.The energy of system in final state is calculated.It is found that for the two-dimensional Ising system,there are two final States--ground state and stripe state.The energy of ground state is 0,and that of stripe state is approximately 2/L because the number of boundaries between domains mainly is 2.It is also found that the energy of the system in final state can be written as 2/3L.5.The effect of the Metropolis algorithm and Constraint one on dynamical evolution is also discussed.Comparing With Glauber algorithm,we find that the effect of the Constraint algorithm is stronger than that of the Metropolis algorithm.