We investigate the critical short-time scaling of the two-dimensional lattice ϕ4 field theory with a Langevin dynamics. Starting from a "hot" initial configuration but with a small magnetization, the critical initial increase of the magnetization is observed, through which we determine the critical point. From the short-time relaxation dynamics of various quantities at the critical point obtained, the dynamic critical exponents θ, z and the static exponent β/ν are evaluated. In executing a Langevin simulation, an appropriate discretization method with respect to the time degree of freedom becomes essentially important to be adopted and we show that the well-known second-order form of discretized Langevin equation works well to investigate the short-time dynamics.We investigate the critical short-time scaling of the two-dimensional lattice ϕ4 field theory with a Langevin dynamics. Starting from a "hot" initial configuration but with a small magnetization, the critical initial increase of the magnetization is observed, through which we determine the critical point. From the short-time relaxation dynamics of various quantities at the critical point obtained, the dynamic critical exponents θ, z and the static exponent β/ν are evaluated. In executing a Langevin simulation, an appropriate discretization method with respect to the time degree of freedom becomes essentially important to be adopted and we show that the well-known second-order form of discretized Langevin equation works well to investigate the short-time dynamics.

International Journal of Modern Physics CMay 1, 20090 citations

Determining critical exponents in small systems

Andrew S. Hirsch

Prepared forJan 1, 19930 citations

SHORT-TIME CRITICAL DYNAMIC PROCESS OF TWO-LAYER ISING MODEL

WU MU-YING, Ye AiJun, LI ZI-BING +2 more

Monte Carlo simulations of critical dynamics has been used to study the short-time process and scaling behavior of two-layer Ising model. The result shows that there are critical points even when the coupling between the two layers is not equal to zero; the short-time dynamic critical exponent θ was determined; the traditional critical exponent 1/νz was estimated also.Our result encouraged the supposition of the existence of the critical line and evidenced that this model was likely a weak universal model.Monte Carlo simulations of critical dynamics has been used to study the short-time process and scaling behavior of two-layer Ising model. The result shows that there are critical points even when the coupling between the two layers is not equal to zero; the short-time dynamic critical exponent θ was determined; the traditional critical exponent 1/νz was estimated also.Our result encouraged the supposition of the existence of the critical line and evidenced that this model was likely a weak universal model.

Acta Physica SinicaJan 1, 20004 citations

Monte Carlo simulations of short-time critical dynamics

Bo Zheng

Computer Physics CommunicationsSep 1, 199910 citations

Monte Carlo simulations and numerical solutions of short-time critical dynamics

B Zheng

arXiv:cond-mat/9910504Physica A Statistical Mechanics and its ApplicationsAug 1, 200028 citations

Deterministic Equations of Motion and Dynamic Critical Phenomena

Bo Zheng, M. Schulz, Steffen Trimper

Taking the two-dimensional ${\ensuremath{\varphi}}^{4}$ 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 second-order 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 $\ensuremath{\theta}$, and the static exponents $\ensuremath{\beta}$ and $\ensuremath{\nu}$ are estimated. The deterministic dynamics with random initial states is in the same universality class as the Monte Carlo dynamics.Taking the two-dimensional ${\ensuremath{\varphi}}^{4}$ 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 second-order 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 $\ensuremath{\theta}$, and the static exponents $\ensuremath{\beta}$ and $\ensuremath{\nu}$ are estimated. The deterministic dynamics with random initial states is in the same universality class as the Monte Carlo dynamics.

arXiv:cond-mat/9909322Physical Review LettersMar 1, 199968 citations

z

, the new exponent $\ensuremath{\theta}$, and the static exponents $\ensuremath{\beta}$ and $\ensuremath{\nu}$ are estimated. The deterministic dynamics with random initial states is in the same universality class as the Monte Carlo dynamics.