Correlated Percolation

Coniglio, Antonio; Fierro, Annalisa

doi:10.1007/978-0-387-30440-3_104

Cited by 15 publications

(22 citation statements)

References 131 publications

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“…We note that it is possible to associate other critical exponents to the jamming transition. This is common within percolation theory where, besides usual critical exponents obeying standard scaling laws, many other critical exponents are introduced, related to quantities, like shortest path, backbone, elastic properties and so on [51][52][53] , reflecting structural properties of the critical clusters. Some of the theoretical predictions, such as the coincidence between ρ k and ρ j , are supported by numerical results, while others are currently difficult to test.…”

Section: Discussionmentioning

confidence: 99%

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Universal behaviour of the glass and the jamming transitions in finite dimensions for hard spheres

2017

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We investigate the glass and the jamming transitions of hard spheres in finite dimensions d, through a revised cell theory, that combines the free volume and the Random First Order Theory (RFOT). Recent results show that in infinite dimension the ideal glass transition and jamming transitions are distinct, while based on our theory we argue that they indeed coincide for finite d. As a consequence, jamming results into a percolation transition described by RFOT, with a static length diverging with exponent ν = 2/d, which we verify through finite size scaling, and standard critical exponents α = 0, β = 0 and γ = 2 independent on d.

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Section: Discussionmentioning

confidence: 99%

“…As the transition is approached the number density of critical clusters vanishes as ξ −d , and the percolation probability jumps discontinuously from 0 to 1. Adapting the standard scaling ansatz [51][52][53] …”

Section: Random First Order Percolation Transitionmentioning

confidence: 99%

Universal behaviour of the glass and the jamming transitions in finite dimensions for hard spheres

2017

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“…Coniglio and collaborators [24,25] presented percolation theory as the generic framework to investigate the distribution of clusters given the distribution of the constitutive elements (here suitable sites), with the underlying idea that geometrical clusters capture the physical properties of the substrate.…”

Section: Size Distribution Of Finite Clustersmentioning

confidence: 99%

“…The pair connectedness function C(r) is defined as the probability that a site at distance r from a suitable origin is suitable and belongs to the same finite cluster (the infinite cluster has to be removed from the computation) [25,24]. Statistical isotropy of the model ensures that C(r) depends only on the modulus r.…”

Section: Pair Connectedness Function C(r)mentioning

confidence: 99%

“…The threshold value p c has been determined for a variety of infinite lattices, with p c 0.592 in a square lattice [1]. Models of correlated percolation conversely consider that the probability of a site being suitable depends on the status of its neighbors [25]. Another archetypal model of statistical physics, the Ising model, is based on local particle interactions resulting in patterns of spatially correlated structures [28,29].…”

Section: Introductionmentioning

confidence: 99%

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Correlated percolation models of structured habitat in ecology

Huth

Lesne

Munoz³

et al. 2014

Physica A: Statistical Mechanics and its Applications

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Percolation offers acknowledged models of random media when the relevant medium characteristics can be described as a binary feature. However, when considering habitat modeling in ecology, a natural constraint comes from nearest-neighbor correlations between the suitable/unsuitable states of the spatial units forming the habitat. Such constraints are also relevant in the physics of aggregation where underlying processes may lead to a form of correlated percolation. However, in ecology, the processes leading to habitat correlations are in general not known or very complex. As proposed by Hiebeler [Ecology 81, 1629[Ecology 81, (2000], these correlations can be captured in a lattice model by an observable aggregation parameter q, supplementing the density p of suitable sites. We investigate this model as an instance of correlated percolation. We analyze the phase diagram of the percolation transition and compute the cluster size distribution, the pair-connectedness function C(r) and the correlation function g(r). We find that while g(r) displays a power-law decrease associated with long-range correlations in a wide domain of parameter values, critical properties are compatible with the universality class of uncorrelated percolation. We contrast the correlation structures obtained respectively for the correlated percolation model and for the Ising model, and show that the diversity of habitat configurations generated by the Hiebeler model is richer than the archetypal Ising model. We also find that emergent structural properties are peculiar to the implemented algorithm, leading to questioning the notion of a well-defined model of aggregated habitat. We conclude that the choice of model and algorithm have strong consequences on what insights ecological studies can get using such models of species habitat.

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Amorphous Order and Nonlinear Susceptibilities in Glassy Materials

2021

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We review 15 years of theoretical and experimental work on the nonlinear response of glassy systems. We argue that an anomalous growth of the peak value of nonlinear susceptibilities is a signature of growing “amorphous order” in the system, with spin-glasses as a case in point. Experimental results on supercooled liquids are fully compatible with the random first-order transition (RFOT) prediction of compact “glassites” of increasing volume as temperature is decreased, or as the system ages. We clarify why such a behavior is hard to explain within purely kinetic theories of glass formation, despite recent claims to the contrary.

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Correlated Percolation

Cited by 15 publications

References 131 publications

Universal behaviour of the glass and the jamming transitions in finite dimensions for hard spheres

Universal behaviour of the glass and the jamming transitions in finite dimensions for hard spheres

Correlated percolation models of structured habitat in ecology

Amorphous Order and Nonlinear Susceptibilities in Glassy Materials

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