A method is proposed to determine the dynamical critical exponent. The method is based on the scaling for dynamical hysteresis resulted from a linearly swept field. We prove that in model $A$ dynamical hysteresis scaling at critical temperature is universal. The nearest-neighbor Ising models are used to demonstrate such concepts and the dynamical critical exponents can be determined accurately. We also propose a universal relation between static and dynamical critical exponents in Ising class in single-spin-flip dynamics.A method is proposed to determine the dynamical critical exponent. The method is based on the scaling for dynamical hysteresis resulted from a linearly swept field. We prove that in model $A$ dynamical hysteresis scaling at critical temperature is universal. The nearest-neighbor Ising models are used to demonstrate such concepts and the dynamical critical exponents can be determined accurately. We also propose a universal relation between static and dynamical critical exponents in Ising class in single-spin-flip dynamics.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsAug 1, 199812 citations

Spectral Methods Applied to Ising Models

B. DeFacio, C. L. Hammer, J. Ely Shrauner

Springer eBooksJan 1, 19800 citations

Static critical exponents from the dynamics of damage spreading and overhangs in the Ising model with temperature gradient

G. G. Batrouni, Alex Hansen

By studying damage spreading in spin models in a temperature gradient, it is possible to determine not only the critical temperature, and the correlation length exponent v, but also a second critical exponent beta with high precision. This is done by studying the dynamics of damage spreading, in particular the overhangs which develop in the damage front. The authors demonstrate the method for the two-dimensional Ising model using heat bath dynamics, and discuss differences with Metropolis dynamics.By studying damage spreading in spin models in a temperature gradient, it is possible to determine not only the critical temperature, and the correlation length exponent v, but also a second critical exponent beta with high precision. This is done by studying the dynamics of damage spreading, in particular the overhangs which develop in the damage front. The authors demonstrate the method for the two-dimensional Ising model using heat bath dynamics, and discuss differences with Metropolis dynamics.

Journal of Physics A Mathematical and GeneralSep 7, 19929 citations

The dynamic critical exponent of the three-dimensional Ising model

R. Matz, D. L. Hunter, Naeem Jan

Journal of Statistical PhysicsFeb 1, 199434 citations

Dynamical Critical Exponent of Ising Systems: An Extension of Thompson's Approach

P. R. Silva

physica status solidi (b)Aug 1, 19912 citations

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

A method is proposed to determine the dynamical critical exponent. The method is based on the scaling for dynamical hysteresis resulted from a linearly swept field. We prove that in model

A

dynamical hysteresis scaling at critical temperature is universal. The nearest-neighbor Ising models are used to demonstrate such concepts and the dynamical critical exponents can be determined accurately. We also propose a universal relation between static and dynamical critical exponents in Ising class in single-spin-flip dynamics.