Values of dynamic critical exponents are numerically estimated for various models with the nonequilibrium relaxation method to test the dynamic universality hypothesis. The dynamics used here are single-spin update with Metropolis-type transition probabities. The estimated values of nonequilibrium relaxation exponent of magnetization λ m (=β/ z ν) of Ising models on bcc and fcc lattices are estimated to be 0.251(3) and 0.252(3), respectively, which are consistent with the value of the model on simple-cubic lattice, 0.250(2). The dynamic critical exponents of three-states Potts models on square, honeycomb and triangular lattices are also estimated to be 2.193(5), 2.198(4), and 2.199(3), respectively. They are consistent within the error bars. It is also confirmed that Ising models with regularly modulated coupling constants on square lattice have the same dynamic critical exponents with the uniformly ferromagnetic Ising model.Values of dynamic critical exponents are numerically estimated for various models with the nonequilibrium relaxation method to test the dynamic universality hypothesis. The dynamics used here are single-spin update with Metropolis-type transition probabities. The estimated values of nonequilibrium relaxation exponent of magnetization λ m (=β/ z ν) of Ising models on bcc and fcc lattices are estimated to be 0.251(3) and 0.252(3), respectively, which are consistent with the value of the model on simple-cubic lattice, 0.250(2). The dynamic critical exponents of three-states Potts models on square, honeycomb and triangular lattices are also estimated to be 2.193(5), 2.198(4), and 2.199(3), respectively. They are consistent within the error bars. It is also confirmed that Ising models with regularly modulated coupling constants on square lattice have the same dynamic critical exponents with the uniformly ferromagnetic Ising model.

Journal of the Physical Society of JapanDec 25, 200717 citations

Critical dynamics of the three-dimensional Ising model: A Monte Carlo study

Hans-Otto Heuer

Journal of Statistical PhysicsAug 1, 199312 citations

Numerical simulations for the Ising model on three dimensional lattices with coordination number equal 5: static and dynamic critical phenomena

Lourdes Bibiana Merino-Solís, Francisco Sastre

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 $ν$ , $γ$ and $β$ . 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 $z=2.037(8)$ , the exponent for the autocorrelation $λ/z=1.364(5)$ , the exponent of the critical initial increase $θ'=0.109(8)$ and the asymptotic value of the fluctuation-dissipation ratio $X^\infty=0.433(1)$ . All of these results are in good agreement to the previous values reported for the 3D Ising model universality class.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 $ν$, $γ$ and $β$. 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 $z=2.037(8)$, the exponent for the autocorrelation $λ/z=1.364(5)$, the exponent of the critical initial increase $θ'=0.109(8)$ and the asymptotic value of the fluctuation-dissipation ratio $X^\infty=0.433(1)$. All of these results are in good agreement to the previous values reported for the 3D Ising model universality class.

arXiv:2406.18782Jun 26, 20240 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

Crossover Critical Behavior in the Three-Dimensional Ising Model

Young C. Kim, Mikhail A. Anisimov, Jan V. Sengers +1 more

arXiv:cond-mat/0203190Journal of Statistical PhysicsMar 1, 200349 citations

ν

γ

and

β

. 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)

, the exponent for the autocorrelation

λ/z=1.364(5)

, the exponent of the critical initial increase

θ'=0.109(8)

and the asymptotic value of the fluctuation-dissipation ratio

X^\infty=0.433(1)

. All of these results are in good agreement to the previous values reported for the 3D Ising model universality class.