6533b853fe1ef96bd12abf98

RESEARCH PRODUCT

Monte Carlo study of the ising model phase transition in terms of the percolation transition of “physical clusters”

subject

description

Finite squareL×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energyU, specific heatC, magnetization 〈|M|〉, susceptibilityχ) and percolation cluster properties relating to the “physical clusters,” namely the Fortuin-Kasteleyn clusters (percolation probability 〈P∞〉, percolation susceptibilityχp, cluster size distributionnl) 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 fromχ even in the thermodynamic limit, since a fluctuation in the size of the percolating net contributes toχ, but not toχp. NearTc 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.