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  • Monte Carlo simulation  (3)
  • Finite-size scaling  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Monte Carlo study of the ising model phase transition in terms of the percolation transition of “physical clusters” (1990)
    Springer
    Journal of statistical physics 60 (1990), S. 585-618 
    Details
    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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  • 2
    Electronic Resource
    Electronic Resource
    Finite-size effects at critical points with anisotropic correlations: Phenomenological scaling theory and Monte Carlo simulations (1989)
    Springer
    Journal of statistical physics 55 (1989), S. 87-126 
    Details
    ISSN: 1572-9613
    Keywords: Finite-size scaling ; anisotropic systems ; Lifshitz points ; driven Kawasaki model ; nonequilibrium phase transitions ; Monte Carlo simulations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Various thermal equilibrium and nonequilibrium phase transitions exist where the correlation lengths in different lattice directions diverge with different exponentsv ‖,v ⊥: uniaxial Lifshitz points, the Kawasaki spin exchange model driven by an electric field, etc. An extension of finite-size scaling concepts to such anisotropic situations is proposed, including a discussion of (generalized) rectangular geometries, with linear dimensionL ‖ in the special direction and linear dimensionsL ⊥ in all other directions. The related shape effects forL ‖≠L ⊥ but isotropic critical points are also discussed. Particular attention is paid to the case where the generalized hyperscaling relationv ‖+(d−1)v ⊥=γ+2β does not hold. As a test of these ideas, a Monte Carlo simulation study for shape effects at isotropic critical point in the two-dimensional Ising model is presented, considering subsystems of a 1024x1024 square lattice at criticality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01042592
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  • 3
    Electronic Resource
    Electronic Resource
    Monte Carlo simulation of many-arm star polymers in two-dimensional good solvents in the bulk and at a surface (1991)
    Springer
    Journal of statistical physics 64 (1991), S. 781-806 
    Details
    ISSN: 1572-9613
    Keywords: Monte Carlo simulation ; polymer ; star polymer ; polymer network ; self-avoiding walk ; two dimensions ; critical exponent ; surface adsorption ; radial distribution function ; total number of configurations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A Monte Carlo technique is proposed for the simulation of statistical properties of many-arm star polymers on lattices. In this vectorizing algorithm, the length of each arml is increased by one, step by step, from a starting configuration withl=1 orl=2 which is generated directly. This procedure is carried out for a large sample (e.g., 100,000 configurations). As an application, we have studied self-avoiding stars on the square lattice with arm lengths up tol max=125 and up tof=20 arms, both in the bulk and in the geometry where the center of the star is adsorbed on a repulsive surface. The total number of configurations, which behaves asN∼l γ G–1μ fl , whereμ=2.6386 is the usual effective coordination number for self-avoiding walks on the square lattice, is analyzed, and the resulting exponentsγ G=γ(f) andγ s (f) for the bulk and surface geometries are found to be compatible with predictions of Duplantier and Saleur based on conformai invariance methods. We also obtain distribution functions for the monomer density and the distance of the end of an arm from its center. The results are consistent with a scaling theory developed by us.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01048315
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  • 4
    Electronic Resource
    Electronic Resource
    Monte Carlo simulation of phase separation and clustering in the ABV model (1991)
    Springer
    Journal of statistical physics 62 (1991), S. 161-175 
    Details
    ISSN: 1572-9613
    Keywords: Phase separation ; clusters ; Monte Carlo simulation ; vacancy diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract As a model for a binary alloy undergoing an unmixing phase transition, we consider a square lattice where each site can be either taken by an A atom, a B atom, or a vacancy (V), and there exists a repulsive interaction between AB nearest neighbor pairs. Starting from a random initial configuration, unmixing proceeds via random jumps of A atoms or B atoms to nearest neighbor vacant sites. In the absence of any interaction, these jumps occur at jump ratesΓ A andΓ B, respectively. For a small concentration of vacancies (c v=0.04) the dynamics of the structure factorS(k,t) and its first two momentsk 1(t),k 2 2 (t) is studied during the early stages of phase separation, for several choices of concentrationc B of B atoms. Forc B=0.18 also the time evolution of the cluster size distribution is studied. Apart from very early times, the mean cluster sizel(t) as well as the moments of the structure function depend on timet and the ratioΓ of the jump rates (Γ=Γ B/Γ A) only via a scaled timet/τ(Γ). Qualitatively, the behavior is very similar to the direct exchange model containing no vacancies. Consequences for phase separation of real alloys are briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01020864
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