New method for constructing phase diagrams in 2D centered tetragonal Ising nanoparticles using the cellular automata approach

In this study, both ferromagnetic and antiferromagnetic spin configurations of a 2D-centered tetragonal Ising nanoparticle with two types of exchange interactions (J and Jr) are considered. A newly introduced algorithm using Cellular Automata simulation method, which is relied on counting the states with a magnitude of magnetization per site exceeding a threshold value m_t, is used to compute the value of the reduced critical temperature. The sensitivity of the critical temperature value to the lattice size and exchange interactions (The ratio of Jr/J denoted by r parameter) are examined. The results show that the value of the critical temperature increases with increasing lattice size with a decreasing slope. Moreover, the same behavior was observed in ferromagnetic and antiferromagnetic cases.