MONTE-CARLO STUDY OF THE ISING-MODEL PHASE-TRANSITION IN TERMS OF THE PERCOLATION TRANSITION OF PHYSICAL CLUSTERS

Finite square L×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energy U, specific heat C, magnetization 〈|M|〉, susceptibility χ) and percolation cluster properties relating to the "physical clusters," namely the Fortuin-Kasteleyn clusters (percolation probability 〈P∞〉, percolation susceptibility χp, cluster size distribution nl) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, 〈P∞〉 being identical to 〈|M|〉 in the thermodynamic limit, while finite-size corrections differ. In contrast, χp differs from χ even in the thermodynamic limit, since a fluctuation in the size of the percolating net contributes to χ, but not to χp. Near Tc the cluster size distribution has the scaling properties as hypothesized by earlier phenomenological theories. We also present a generalization of the Swendsen-Wang algorithm allowing one to cross over continuously to the Glauber dynamics. © 1990 Plenum Publishing Corporation.