Ising model for an incompletely occupied two­-dimensional square lattice

Abstract

We studied the Ising model for a square lattice whose occupation of sites by the Ising spins depends on a probability of occupancy ρ. We found out that as ρ decreases, the transition temperature for magnetization M in the absence of external magnetic field also decreases. This behavior was explained in view of the concepts of von Neumann neighborhood and the Monte Carlo spin flipping rule used in the calculation of M. We also referred to these concepts to create a plausibility argument intending to falsify a probable conception that the transition temperature should abruptly change with respect to ρ at around the percolation critical probability of occupancy.