ISSN:
1572-9613
Keywords:
Percolation
;
“physical clusters”
;
Ising model
;
Monte Carlo simulation
;
finite-size scaling
;
Fortuin-Kasteleyn representation
;
Swendsen-Wang algorithm
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract 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 susceptibilityχ p, cluster size distributionn l) 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,χ p differs fromχ even in the thermodynamic limit, since a fluctuation in the size of the percolating net contributes toχ, but not toχ p. NearT c 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01025984
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