This work presents short-time Monte Carlo simulations for the two dimensional Majority-vote model starting from ordered and disordered states. It has been found that there are two pseudo-critical points, each one within the error-bar range of previous reported values performed using fourth order cumulant crossing method. The results show that the short-time dynamic for this model has a dependence on the initial conditions. Based on this dependence a method is proposed for the evaluation of the pseudo critical points and the extraction of the dynamical critical exponent $z$ and the static critical exponent $β/ν$ for this model.This work presents short-time Monte Carlo simulations for the two dimensional Majority-vote model starting from ordered and disordered states. It has been found that there are two pseudo-critical points, each one within the error-bar range of previous reported values performed using fourth order cumulant crossing method. The results show that the short-time dynamic for this model has a dependence on the initial conditions. Based on this dependence a method is proposed for the evaluation of the pseudo critical points and the extraction of the dynamical critical exponent $z$ and the static critical exponent $β/ν$ for this model.

arXiv:1001.0163Dec 31, 20090 citations

Monte Carlo simulations of short-time critical dynamics

Bo Zheng

Computer Physics CommunicationsSep 1, 199910 citations

Universal short-time quantum critical dynamics of finite-size systems

Yu-Rong Shu, Shuai Yin, Dao‐Xin Yao

We investigate the short-time quantum critical dynamics in the imaginary-time relaxation processes of finite-size systems. Universal scaling behaviors exist in the imaginary-time evolution. In particular, the system undergoes a critical initial slip stage characterized by an exponent $\ensuremath{\theta}$, in which an initial power-law increase emerges in the imaginary-time correlation function when the initial state has a zero order parameter and a vanishing correlation length. Under different initial conditions, the quantum critical point and critical exponents can be determined from the universal scaling behaviors. We apply the method to the one- and two-dimensional transverse field Ising models using quantum Monte Carlo (QMC) simulations. In the one-dimensional case, we locate the quantum critical point at ${(h/J)}_{c}=1.000\phantom{\rule{0.16em}{0ex}}03(8)$ in the thermodynamic limit, and we estimate the critical initial slip exponent $\ensuremath{\theta}=0.3734(2)$ and the static exponent $\ensuremath{\beta}/\ensuremath{\nu}=0.1251(2)$ by analyzing data on chains of length $L=32--256$ and 48--256, respectively. For the two-dimensional square-lattice system, the critical coupling ratio is given by $3.044\phantom{\rule{0.16em}{0ex}}51(7)$ in the thermodynamic limit, while the critical exponents are $\ensuremath{\theta}=0.209(4)$ and $\ensuremath{\beta}/\ensuremath{\nu}=0.518(1)$ estimated by data on systems of size $L=24$ --64 and 32--64, respectively. Remarkably, the critical initial slip exponents obtained in both models are notably distinct from their classical counterparts due to the essential differences between classical and quantum dynamics. The short-time critical dynamics and the imaginary-time relaxation QMC approach can be readily adapted to various models.We investigate the short-time quantum critical dynamics in the imaginary-time relaxation processes of finite-size systems. Universal scaling behaviors exist in the imaginary-time evolution. In particular, the system undergoes a critical initial slip stage characterized by an exponent $\ensuremath{\theta}$, in which an initial power-law increase emerges in the imaginary-time correlation function when the initial state has a zero order parameter and a vanishing correlation length. Under different initial conditions, the quantum critical point and critical exponents can be determined from the universal scaling behaviors. We apply the method to the one- and two-dimensional transverse field Ising models using quantum Monte Carlo (QMC) simulations. In the one-dimensional case, we locate the quantum critical point at ${(h/J)}_{c}=1.000\phantom{\rule{0.16em}{0ex}}03(8)$ in the thermodynamic limit, and we estimate the critical initial slip exponent $\ensuremath{\theta}=0.3734(2)$ and the static exponent $\ensuremath{\beta}/\ensuremath{\nu}=0.1251(2)$ by analyzing data on chains of length $L=32--256$ and 48--256, respectively. For the two-dimensional square-lattice system, the critical coupling ratio is given by $3.044\phantom{\rule{0.16em}{0ex}}51(7)$ in the thermodynamic limit, while the critical exponents are $\ensuremath{\theta}=0.209(4)$ and $\ensuremath{\beta}/\ensuremath{\nu}=0.518(1)$ estimated by data on systems of size $L=24$--64 and 32--64, respectively. Remarkably, the critical initial slip exponents obtained in both models are notably distinct from their classical counterparts due to the essential differences between classical and quantum dynamics. The short-time critical dynamics and the imaginary-time relaxation QMC approach can be readily adapted to various models.

arXiv:1705.05931Physical review. B./Physical review. BSep 12, 201717 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

Short-time critical dynamics of the three-dimensional Ising model

A Jaster, J. Mainville, L Schülke +1 more

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.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.

arXiv:cond-mat/9808131Journal of Physics A Mathematical and GeneralJan 1, 199976 citations

Determination of the critical point and exponents from short-time dynamics

Lothar Schülke, Bo Zheng

arXiv:cond-mat/9510109Physics Letters AMay 1, 199645 citations

z

and the static critical exponent

β/ν

for this model.

{(h/J)}_{c}=1.000\phantom{\rule{0.16em}{0ex}}03(8)

in the thermodynamic limit, and we estimate the critical initial slip exponent $\ensuremath{\theta}=0.3734(2)$ and the static exponent $\ensuremath{\beta}/\ensuremath{\nu}=0.1251(2)$ by analyzing data on chains of length

L=32--256

and 48--256, respectively. For the two-dimensional square-lattice system, the critical coupling ratio is given by

3.044\phantom{\rule{0.16em}{0ex}}51(7)

in the thermodynamic limit, while the critical exponents are $\ensuremath{\theta}=0.209(4)$ and $\ensuremath{\beta}/\ensuremath{\nu}=0.518(1)$ estimated by data on systems of size

L=24

--64 and 32--64, respectively. Remarkably, the critical initial slip exponents obtained in both models are notably distinct from their classical counterparts due to the essential differences between classical and quantum dynamics. The short-time critical dynamics and the imaginary-time relaxation QMC approach can be readily adapted to various models.