Distribution of fractal clusters and scaling in the Ising model

Cambier, Jean-Luc; Nauenberg, Michael

doi:10.1103/physrevb.34.8071

Cited by 49 publications

(40 citation statements)

References 17 publications

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“…This seems to correspond to the estimated exponent for percolating clusters [29,30], τ = 2 + confirmation of the critical nature of our observations. In this section we have shown that clusters at T * (L) show, rather remarkably, both scale free behaviour, and a separation of scales: Typical cluster size, maximum secondary cluster size and spanning cluster size are all fixed by L, however their amplitudes are sufficiently different to ensure a minimum of interference between the three scales.…”

Section: Cluster Sizes and Distributionsupporting

confidence: 89%

Criterion for universality-class-independent critical fluctuations: Example of the two-dimensional Ising model

2004

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Order parameter fluctuations for the two dimensional Ising model in the region of the critical temperature are presented. A locus of temperatures T * (L) and of magnetic fields B * (L) are identified, for which the probability density function is similar to that for the 2D-XY model in the spin wave approximation. The characteristics of the fluctuations along these points are largely independent of universality class. We show that the largest range of fluctuations relative to the variance of the distribution occurs along these loci of points, rather than at the critical temperature itself and we discuss this observation in terms of intermittency. Our motivation is the identification of a generic form for fluctuations in correlated systems in accordance with recent experimental and numerical observations. We conclude that a universality class dependent form for the fluctuations is a particularity of critical phenomena related to the change in symmetry at a phase transition.

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Section: Cluster Sizes and Distributionsupporting

confidence: 89%

Criterion for universality-class-independent critical fluctuations: Example of the two-dimensional Ising model

2004

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“…However, this suggested fractal dimension is not consistent with numerical results [7]. The reason is that there are actually two contributions in forming a cluster: One is due to the correlation due to the spin interaction, while the other is a purely geometric contribution which survives even in the infinite-T limit [8].…”

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confidence: 53%

Cluster-size heterogeneity in the two-dimensional Ising model

Baek

et al. 2012

Phys. Rev. E

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We numerically investigate the heterogeneity in cluster sizes in the two-dimensional Ising model and verify its scaling form recently proposed in the context of percolation problems [Phys. Rev. E 84, 010101(R) (2011)]. The scaling exponents obtained via the finite-size scaling analysis are shown to be consistent with theoretical values of the fractal dimension d(f) and the Fisher exponent τ for the cluster distribution. We also point out that strong finite-size effects exist due to the geometric nature of the cluster-size heterogeneity.

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“…As to an intuitive explanation for the postcritical peak in T gl , preliminary research implicates a subtle interplay between differing contributions to T gl from sites within and on the boundaries of same-spin domains, and the change in distribution of domain sizes as the temperature increases and domains disintegrate [22]. A complementary perspective is offered in Ref.…”

Section: Critical Inverse Temperaturementioning

confidence: 99%