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

Abstract: 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 $\nu$, $\gamma$ and $\beta$. 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 $\lambda/z=1.364(5)$, the exponent of the critical initial increase $\theta'=0.109(8)$ 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.