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Dynamic exponent for 2D Ising model by power spectra method

Kwan-tai Leung

We consider power spectra for fluctuating quantities at a critical point, P( omega ) varies as omega - phi , where phi is determined by the dynamic exponent z and static exponents specific to the quantity considered. From the magnetization spectra obtained with simulations, z is found to be 2.13+or-0.03 for the two-dimensional Glauber kinetic Ising model, hence in accord with recent Monte Carlo relaxational studies, but at odds with those obtained by series expansion and damage spreading methods. Excellent dynamic finite-size scaling for system sizes L=10 to 128 supports our estimate.We consider power spectra for fluctuating quantities at a critical point, P( omega ) varies as omega - phi , where phi is determined by the dynamic exponent z and static exponents specific to the quantity considered. From the magnetization spectra obtained with simulations, z is found to be 2.13+or-0.03 for the two-dimensional Glauber kinetic Ising model, hence in accord with recent Monte Carlo relaxational studies, but at odds with those obtained by series expansion and damage spreading methods. Excellent dynamic finite-size scaling for system sizes L=10 to 128 supports our estimate.

Journal of Physics A Mathematical and GeneralDec 7, 19936 citations

Large-scale simulation of the two-dimensional kinetic Ising model

Andreas Linke, Dieter W. Heermann, Peter Altevogt +1 more

arXiv:cond-mat/9509115Physica A Statistical Mechanics and its ApplicationsDec 1, 199524 citations

Monte Carlo renormalization group study of the two dimensional kinetic Ising model

John P. Bartel

Jan 1, 19840 citations

Critical slowing down of the two-dimensional kinetic Ising model with Glauber dynamics

Jian Wang

We calculated the autorelaxation time for the two-dimensional kinetic Ising model with Glauber dynamics using a high-temperature series-expansion technique. The series is analyzed using a differential Pad\'e approximant. The exponent z for critical slowing down is found to be z=2.207\ifmmode\pm\else\textpm\fi{}0.008.

Physical review. B, Condensed matterJan 1, 199323 citations

A scaling approach to critical exponent calculations for the 2D Ising model

Thom Jäderlund

Jan 1, 20200 citations

Non-Markovian global persistence in phase ordering kinetics

Malte Henkel, Michel Pleimling

The persistence probability P g ( t ) of the global order parameter of a simple ferromagnet undergoing phase ordering kinetics after a quench from a fully disordered state to below the critical temperature, T < T c , is analysed. It is argued that the persistence probability decays algebraically with time in the entire low-temperature phase. For Markov processes, the associated global persistence exponent θ g = (2λ C − d )/(2 z ) is related to the autocorrelation exponent λ C . This relationship is confirmed for phase ordering in the exactly solved 1D Ising model and the d -dimensional spherical model. For the 2D Glauber–Ising model, the temperature-independent estimate θ g = 0.063(2) indicates that the dynamics of the global order parameter is described by a non-Markovian process.The persistence probability P g ( t ) of the global order parameter of a simple ferromagnet undergoing phase ordering kinetics after a quench from a fully disordered state to below the critical temperature, T < T c , is analysed. It is argued that the persistence probability decays algebraically with time in the entire low-temperature phase. For Markov processes, the associated global persistence exponent θ g = (2λ C − d )/(2 z ) is related to the autocorrelation exponent λ C . This relationship is confirmed for phase ordering in the exactly solved 1D Ising model and the d -dimensional spherical model. For the 2D Glauber–Ising model, the temperature-independent estimate θ g = 0.063(2) indicates that the dynamics of the global order parameter is described by a non-Markovian process.

arXiv:0907.1642Journal of Statistical Mechanics Theory and ExperimentDec 21, 20096 citations

Simulation of time exponent in 2D Glauber kinetic Ising model

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