Simulation of material magnetization with inhomogeneous external magnetic field based on Ising model

Abstract

It is well known from the Ising Model that the phase transition of magnetic materials depends on the external magnetic field, their neighboring spins, and the interaction strength between spins. In this work, we explore the Ising model for the case where the external magnetic field is zero, homogenous, and in-homogeneous. We show that zero external magnetic field results in a paramagnetic to ferromagnetic phase transition with a strong interaction coupling critical point value whereas a nonzero external magnetic field will shift the critical point value due to a change in the magnetization or energy. We found that a homogeneous and in-homogeneous magnetic field results in a difference in magnetization where for the case of homogeneous magnetic fields, the magnetization and energy are higher compared to the in-homogeneous case. In addition, the external magnetic field will result in an anti-ferromagnetic to ferromagnetic phase transition.