Cluster evolution in a cold Ising ferromagnet: Disappearance of magic numbers with temperature rise

Abstract

Decay and growth of clusters at low and intermediate temperatures based on the two-dimensional square-lattice Ising model has been studied with Monte Carlo simulations employing Glauber (or Metropolis) dynamics, exploiting a procedure where the starting configuration is a cluster (that tend to grow in the applied magnetic field) on a relatively small lattice. The behavior of such a cluster is stochastic and only when typical several thousands of identical clusters are analyzed will the underlying deterministic behavior become apparent. At 0.4T(c), the time-dependent cluster size distribution is relatively broad, but smooth, i.e., Gaussian, and the decay and growth behaviors of various relative compact clusters are compared. At lower temperatures, modulations in the size distribution occur with minima at magic sizes corresponding to n=mxm+1 and n=mx(m+1)+1 with m integer values. A quantitative analysis of the amplitude of the modulations as a function of temperature is performed. Also the relation between the distributions of size and of the number of internal cluster bonds (or cluster perimeter) is scrutinized.