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∞=0.433(1). All of these results are in good agreement to the previous values reported for the 3D Ising model universality class.
We make use of the calculation of Achiam and Kosterlitz and investigate the generalization of the Migdal-type renormalization-group calculation to critical dynamics, by looking at the one- and two-dimensional kinetic Ising model with no conserved magnetization. In the two-dimensional case the dynamical critical index
ZM(magneticperturbation)=2.064 and
ZE(energylikeperturbation)=1.819 for scale factor $\ensuremath{\lambda}=1$.
ZM involves the static $\frac{\ensuremath{\beta}}{\ensuremath{\nu}}$ exponent, while
ZE involves $\frac{1}{\ensuremath{\nu}}$, and therefore, it is not surprising that
ZM is closer to the high-temperature expansion results, since $\frac{\ensuremath{\beta}}{\ensuremath{\nu}}$ in the Migdal approximation for statics is much closer to the exact value than $\frac{1}{\ensuremath{\nu}}$. In one dimension we obtain
ZM=ZE=2, which is the exact result of Glauber.