The two-dimensional site-diluted Ising ferromagnet a damage-spreading analysis

Abstract

The quenched site-diluted Ising ferromagnet on a square lattice, for which each site is occupied or empty with probabilities p and 1 − p, respectively, is studied numerically through damage-spreading procedures. By making use of the Glauber dynamics, the percolation threshold p c is estimated. Within the heat-bath dynamics, the damage-spreading temperatures T d ( p) (for several values of p> p c ) are computed, indicating a strong correlation with the corresponding critical temperatures T c ( p). A procedure for estimating the fractal dimensions of clusters of damaged sites, at low temperatures, is presented; as p → p c , our estimate is very close to 91/48, which is the fractal dimension of the infinite cluster at p = p c in two-dimensional site percolation. Whenever possible to compare, our results are in good agreement with the best estimates available from other techniques, in spite of a modest computational effort.