Construction of phase diagrams for nanoscaled Ising thin films on the honeycomb lattice using cellular automata simulation approach

Effect of Lattice Size on the Critical Temperature of Ising Nanofilms and Nanotubes on the Square Lattice: Cellular Automata Simulation

“…In this paper, for calculation of critical temperature, the described method in references [17,18] is used. In this method, which uses the graph of mean magnetization per site as a function of time for a given temperature, the temperature at which l y l x Figure 2 with Figure 3 of reference [18] shows that the increasing trend of c K for honeycomb lattice up to the size of 500 has been steep.…”

“…x y J J , where x J and y J representing the nearest-neighbor coupling in the l x and l y directions. To updating the lattice sites, the Glauber algorithm with checkerboard techniques are used [17,18]. For this purpose, the sites of lattice were presented by black and white colors, and at each step of the simulation, the white sites will be updated firstly, before the black sites.…”

“…Different theoretical and numerical approaches such as Effective Field Theory (EFT), Monte Carlo, and Cellular Automata (CA) have been used to provide well-tabulated data concerning magnetic properties of magnetic nanostructures [10][11][12][13][14][15][16][17][18][19]. Ising model is one of the best methods for modeling and theoretical study of magnetic materials.…”

“…So far, this subject, the effect of the size and shape on the critical temperature of the Ising nanofilm and nanotube on the square lattice, from the perspective in our work has not been studied, and these results are reported for the first time. The CA method is a simple, fast, and precise method which have used in many cases for studying the Ising model [17,19].…”

“…The average magnetization of the lattice is calculated as follows[17,18]:The average of magnetization per site is calculated as/ m M N < >=< >. In order to increase of accuracy of calculations, in each time step of simulation, the average of magnetization per site is calculated over 200 different samples, as independent computer experiment.…”