Cluster-size heterogeneity in the two-dimensional Ising model

Abstract

We numerically investigate the heterogeneity in cluster sizes in the two-dimensional Ising model and verify its scaling form recently proposed in the context of percolation problems [Phys. Rev. E 84, 010101(R) (2011)]. The scaling exponents obtained via the finite-size scaling analysis are shown to be consistent with theoretical values of the fractal dimension $d_f$ and the Fisher exponent $\tau$ for the cluster distribution. We also point out that strong finite-size effects exist due to the geometric nature of the cluster-size heterogeneity.

10 pages, 4 figures

References in corpus (5)

• Continuity of the Explosive Percolation Transition
• Fractal Structure of Spin Clusters and Domain Walls in 2D Ising Model
• Site Percolation and Phase Transitions in Two Dimensions
• Scaling of cluster heterogeneity in percolation transitions
• Geometric Properties of the Three-Dimensional Ising and XY Models

Cited by in corpus (7)

• Dynamical cluster size heterogeneity
• Domain size heterogeneity in the Ising model: geometrical and thermal transitions
• Emergence of biconnected clusters in explosive percolation
• Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model
• A branching random-walk model of disease outbreaks and the percolation backbone
• Statistics of geometric clusters in the Ising model on a Bethe lattice: statistical mechanics approach
• Statistics of geometric clusters in Potts model: statistical mechanics approach