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arXiv:cond-mat/9808131 · Journal of Physics A Mathematical and General

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

A Jaster, J. Mainville, L Schülke, B Zheng

Published Jan 1, 1999• 76 citations
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Abstract

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.

DOI
10.1088/0305-4470/32/8/008

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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.
The dynamic critical behaviour of the three-dimensional classical Heisenberg model was studied by using short-time Monte Carlo simulations. The dynamic critical exponents z , θ and θ g , as well as the static critical exponents ν and β, were estimated by following the time evolution of the z -component of the total magnetization and its moments of higher order. The anomalous dimension of the magnetization x 0 was also calculated from a relation obtained through finite size scaling in the non-equilibrium stage. Afterwards, the local persistence exponent θ l was obtained by following the power law behaviour of the local persistence probability when the system was quenched from high temperatures to the null one ( T = 0). The time evolution of P l ( t ) was also analysed for T >0 and the expected exponential stretch was observed.
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With Monte Carlo simulations, we investigate short-time critical dynamics of the three-dimensional antiferromagnetic Ising model with a globally conserved magnetization m(s) (not the order parameter). From the power law behavior of the staggered magnetization (the order parameter), its second moment and the autocorrelation, we determine all static and dynamic critical exponents as well as the critical temperature. The universality class of m(s)=0 is the same as that without a conserved quantity, but the universality class of nonzero m(s) is different.
The time evolution of the three-dimensional critical Ising model relaxing from a non-equilibrium 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 behaviour is determined, and the dependence of the long-time linear decay on the initial magnetization, m 0 , is analysed. Our simulation corroborates earlier results derived from continuum models.
In this work we performed numerical simulations for the Ising model on three dimensional lattices with coordination number equal 5. With Monte Carlo simulations in the static case we evaluated the critical temperature and the static critical exponents ννν, γγγ and βββ. Once that we have the critical temperature value we investigated the dynamical critical behavior with Glauber dynamics, starting from disordered states. From our simulations we obtained the values for the dynamic exponent z=2.037(8)z=2.037(8)z=2.037(8), the exponent for the autocorrelation λ/z=1.364(5)λ/z=1.364(5)λ/z=1.364(5), the exponent of the critical initial increase θ′=0.109(8)θ'=0.109(8)θ′=0.109(8) and the asymptotic value of the fluctuation-dissipation ratio X∞=0.433(1)X^\infty=0.433(1)X∞=0.433(1). All of these results are in good agreement to the previous values reported for the 3D Ising model universality class.