Statistical Description of Magnetic Domains in the Two Dimensional Ising Model

=− ∑ with a sum over all neighbouring pairs (z-th component) of spins. Usually it is assumed that the crystal lattice of the ferromagnet is regular and in each site of the lattice the spin with the value S z = –1, or S z = –1 is localized. Two spins i and j interact with each other by the energy –J if both spins are parallel, and +J if they are oposite to each other. Results presented hereafter are obtained by applying Monte Carlo techniques, to the two-dimensional Ising model with periodic boundary conditions. We use the FortuinKasteleyn random cluster model representation of the Ising model [5]. Clusters of the Ising model were generated using the Swenson-Wang algorithm [6]. In this algorithm, clusters of spins are created by introducing bonds between neighbouring spins of the same orientation, with probability 1e xp( / ), B