Critical behavior of the geometrical spin clusters and interfaces in the two-dimensionalthermalized bond Ising model

Abstract

The fractal dimensions and the percolation exponents of geometrical spin clusters of likesign at criticality are obtained numerically for an Ising model with temperaturedependent annealed bond dilution, also known as the thermalized bond Ising model(TBIM), in two dimensions. For this purpose, a modified Wolff single-clusterMonte Carlo simulation is used to generate equilibrium spin configurations onsquare lattices in the critical region. A tie-breaking rule is employed to identifynonintersecting spin cluster boundaries along the edges of the dual lattice. Thevalues obtained for the fractal dimensions of the spanning geometrical clustersDc, and theirinterfaces DI, are in perfect agreement with those reported for the standard two-dimensional ferromagneticIsing model. Furthermore, the variance of the winding angles results in a diffusivityκ = 3 for the two-dimensional thermalized bond Ising model, thus placing it in the universalityclass of the regular Ising model. A finite-size scaling analysis of the largest geometricalclusters results in a reliable estimation of the critical percolation exponents forthe geometrical clusters in the limit of an infinite lattice size. The percolationexponents thus obtained are also found to be consistent with those reported for theregular Ising model. These consistencies are explained in terms of the Fisherrenormalization relations, which express the thermodynamic critical exponentsof systems with annealed bond dilution in terms of those of the regular modelsystem.