Investigation of Size and Shape Dependencies of Phase Diagrams of the Ising Nanofilms and Nanotubes on the Honeycomb Lattice Using Cellular Automata Simulation Approach

Abstract

Size and shape dependencies of phase diagrams of the Ising nanofilms and nanotubes on the honeycomb lattice are investigated by means of probabilistic cellular automata simulation based on Glauber algorithm. The values of reduced critical temperature, K c = k B T c/J (where k B and J are the Boltzmann constant and nearest-neighbor coupling, respectively), for both nanofilms and nanotubes, are obtained at the different sizes of the lattices and the dependency of K c to the number of layers is studied. By increasing the number of layers K c increases but for number of layer more than 8, the critical temperature increases very slowly. We have shown that between two isotropic nanotubes with the same number of spins, the ones with greater diameter (more spins on the edge) have larger critical temperature. For equal size of lattices, the obtained values of K c for nanotube are greater than the nanofilm, but for large sizes, this difference disappears.