Cluster behavior in a finite 2D Ising model with central blocked regions

Abstract

We simulate a 2D ferromagnetic Ising model in a square lattice with non-periodic or finite boundary conditions. We implemented the Monte Carlo Metropolis algorithm to simulate the possible spin configurations of a square lattice with a central region without spins. The resulting magnetic domains of the system were investigated under varying sizes of the blocked region and at different temperature points. It was then observed that higher number of clusters, but of smaller cluster size, occur at high temperatures. Meanwhile, the number of positive and negative spins become almost equal beyond the critical temperature, however, no discernible trend could be observed in the spin up and spin down cluster distribution.