Gaussian free field in the iso-height random islands tuned by percolation model

Cheraghalizadeh, J.; Najafi, M. N.; Mohammadzadeh, Hosein

doi:10.1088/1742-5468/aad6c9

Cited by 9 publications

(7 citation statements)

References 67 publications

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“…7 using the self-consistent iteration method. The RCP has often been employed as a model to be combined with many other dynamical models, like the percolation [41] and Ising [42] models. For a good review of RCP model see [43].…”

Section: -Isingmentioning

confidence: 99%

“…In this section the pores quality are supposed to be described by the relation 9 whose correlations are proved to be [41,42] h( x…”

Section: Ip On Random Coulomb Potential (Rcp)mentioning

confidence: 99%

“…This model is equivalent to scale invariant rough surface with zero roughness exponent. The properties of some dynamical models on (RCP)correlated supports are already done [41,42].…”

Section: Ip On Random Coulomb Potential (Rcp)mentioning

confidence: 99%

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Invasion percolation in short-range and long-range disorder background

Najafi,

Tizdast,

Cheraghalizadeh

et al. 2021

Preprint

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In this paper we investigate the invasion percolation (IP) in imperfect support in which the configuration of imperfections is considered to be correlated. Three lattice models were engaged to realize this pattern: site percolation, Ising model and random coulomb potential (RCP). The first two models are short range interaction (SRI), whereas the last one includes coulomb like interactions which is pretty long range (long-range interactions, LRI). By examining various dynamical observables we show that the critical exponents of SRI IP are robust against the control parameters (temperature in the Ising model and occupation probability in site percolation), whereas its properties in the LRI (RCP) supports are completely different from the normal IP (i.e. on the regular lattice). Especially the fractal dimension of the external frontier of the largest hole converges to 1.099 ± 0.008 for RCP IP, whereas it is nearly 4 3 for SRI IP being compatible with normal IP. Additionally a novel dynamical crossover is seen in the RCP IP according to which the time dependence of all of the observables is divided to three parts: the power-law (small times), the logarithmic (mid time), and the linear (long time) regimes. The second crossover time is shown to go to infinity in the thermodynamic limit, whereas the first crossover time is nearly unchanged, signaling the dominance of the logarithmic regime. The observables become nearly constant in the thermodynamic limit for the long time, showing that it is a stationary phase.

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Section: -Isingmentioning

confidence: 99%

“…In this section the pores quality are supposed to be described by the relation 9 whose correlations are proved to be [41,42] h( x…”

Section: Ip On Random Coulomb Potential (Rcp)mentioning

confidence: 99%

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Invasion percolation in short-range and long-range disorder background

Najafi,

Tizdast,

Cheraghalizadeh

et al. 2021

Preprint

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“…A large class of rough surfaces is called Gaussian surfaces, for which the distribution function of the fluctuating field is Gaussian, and the exponent of the loop Green function is conjectured to be x l = 1 2 [28]. Other electronic system examples are the electron-hole puddles in Graphene [29,30] superconductivity in YBCO compounds [31] and Gaussian free fields [32,33] are known to be non-Gaussian. For a good review see [34].…”

Section: Introductionmentioning

confidence: 99%

Mapping cumulus clouds to scale invariant rough surfaces

Cheraghalizadeh¹,

Tizdast²,

Mohammadzade³

et al. 2022

Preprint

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Motivated by a recent observation on the self-organized criticality of cumulus clouds (Phys. Rev E 103, 052106, 2021) we study their connection to self-similar rough surfaces, in which f ≡ log I plays the role of the main field, where I is the intensity of the received visible light. By simulating the light scattering based on a coarse-grained phenomenological model in a two-dimensional cloud, we argue the possible connection of I to the actual cloud thickness. Although in the vertical incident light f is proportional to the cloud thickness, in the general case it is complected. We study the statistical properties of observational data for f with a focus on the conventional exponents of this scale-invariant rough surface. By calculating the roughness exponents, and comparing them with other exponents like the fractal dimension of loops, the distribution function of the radius of gyration and loop lengths, and the exponent of the green function, we prove that this surface is unconventional in the sense that it is the non-Gaussian self-affine random surface which violates the Kondev hyper-scaling relations.

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“…Correlations in environmental imperfections, as an inevitable fact, have considerable impacts in critical phenomena. Important examples are the self-avoiding walk (SAW) in uncorrelated and Ising-correlated percolation lattices [1], the Bak-Tang-Weisenfeld model (BTW) sandpile model on uncorrelated [2] and Ising-correlated [3] percolation lattices, and the Gaussian free field in the background of metallic nanoparticles [4]. The problem of superdiffusion and subdiffusion processes, and the corresponding correlated random walks on correlated and uncorrelated landscapes, has received attention within the literature to describe many physical scenarios, mostly for crowded systems [5,6].…”

Section: Introductionmentioning

confidence: 99%

Correlation effects in the diluteness pattern in non-integral dimensional systems on $\nu =\displaystyle \frac{4}{5}$ superdiffusion process

Cheraghalizadeh¹,

Najafi²

2019

Phys. Scr.

Self Cite

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The effect of the correlations in the diluteness pattern in the systems with non-integral dimensionality, on ν = 4 5 superdiffusion process is considered in this paper. These spatial correlations have proved to be very effective in the critical phenomena. To simulate the particles motion in this process, we employ the loop erased random walk (LERW). The spatial correlations between imperfections (site-diluteness) also have been modeled by the Ising model on a square lattice. It models the forbidden regions into which the particles are not allowed to enter. The correlations are controlled by an artificial temperature T . The trace of the walkers is shown to be self-similar, whose fingerprint is the power-law behaviors. The detailed analysis of the random walker's traces reveal that the (Ising-type) correlations affect their geometrical properties. At the critical artificial temperature Tc we observe that the exponent of end-to-end distance ν becomes 0.807 ± 0.002. The fractal dimension of the walker's trace is the other geometrical quantity which scales inversely with the square root of the correlation length of the Ising model, i.e. D f (T ) − D f (Tc) ∼ ζ −α in which α = 0.43 ± 0.05. The winding angle test also reveals that the traces are compatible with the Schramm-Loewner evolution theory, and the diffusivity parameter for T = Tc is κ = 1.89 ± 0.05.

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Gaussian free field in the iso-height random islands tuned by percolation model

Cited by 9 publications

References 67 publications

Invasion percolation in short-range and long-range disorder background

Invasion percolation in short-range and long-range disorder background

Mapping cumulus clouds to scale invariant rough surfaces

Correlation effects in the diluteness pattern in non-integral dimensional systems on $\nu =\displaystyle \frac{4}{5}$ superdiffusion process

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