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

TL;DR

This paper performs numerical simulations of the 3D Ising model on lattices with coordination number 5, evaluating static and dynamic critical phenomena, and finds results consistent with known universality class values.

Contribution

It provides new numerical estimates of static and dynamic critical exponents for the Ising model on a less common lattice structure with coordination number 5.

Findings

Critical temperature and static exponents evaluated

Dynamic critical exponents obtained with Glauber dynamics

Results agree with known universality class values

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.