Universality split in absorbing phase transition with conserved field on fractal lattices

Lee, Sang-Gui; Lee, Sang B.

doi:10.1103/physreve.77.041122

Cited by 7 publications

(8 citation statements)

References 37 publications

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“…From the list of exponents, one important thing to notice is that for the existing results α = β/ν , but z = ν /ν ⊥ . This violation of scaling has been reported earlier [11]. There are also several other examples of scaling violation [9,17] in the literature, particularly in one of the two scaling relations mentioned above.…”

Section: Scaling Violation and Its Resolutionsupporting

confidence: 79%

“…In this article we have studied a simple model, Conserved Lattice Gas (CLG) in 1D. For this model it has been claimed earlier [11] that the asymptotic decay exponent is α = 1/4 and the scaling relation α = β/ν is satisfied, but z = ν /ν ⊥ is violated. Here we clearly show that α depends on the choice of initial condition (i.c.…”

mentioning

confidence: 99%

“…To obtain ν from the supercritical data, we use the convenient form ρ a (t, ∆, ∞) = ρ a k(t∆ ν ) which do not require estimate for α, where ρ a is the stationary value of ρ a (t), and k is the scaling function. The existing results [11] for the static and dynamic critical exponents of 1D CLG are listed in table I.…”

mentioning

confidence: 99%

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Dependence of asymptotic decay exponents on initial condition and the resulting scaling violation

Bondyopadhyay

2013

Phys. Rev. E

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There are several examples which show that the critical exponents can be dependent on the initial condition of the system. In such situations, there are many systems where various issues related to the universal behavior, e.g., the existence of universality, the splitting of the universality class, scaling violations, whether the initial dependence should persist even after a sufficiently long time or is a transient effect, the reasons for such features, etc. are not yet quite clear. In this article, with the simple example of the conserved lattice gas model (CLG), we investigate such issues and clearly show that under certain situations the asymptotic decay exponents are, in fact, dependent on the initial condition of the system. We show that such an effect arises because of the existence of two competing time scales and identify the initial conditions which capture the universal features of the system.

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Section: Scaling Violation and Its Resolutionsupporting

confidence: 79%

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confidence: 99%

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Dependence of asymptotic decay exponents on initial condition and the resulting scaling violation

Bondyopadhyay

2013

Phys. Rev. E

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“…In one spatial dimension an active site has at most one neighboring vacant site, leading to deterministic hopping sequences of active particles. As a consequence the transition becomes trivial in this case and is characterized by integer exponents [25]. As a way out, Oliveira proposed to study the CLG on a ladder [26].…”

Section: Conserved Lattice Gas (Clg)mentioning

confidence: 99%

Fixed-Energy Sandpiles Belong Generically to Directed Percolation

et al. 2012

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Fixed-energy sandpiles with stochastic update rules are known to exhibit a nonequilibrium phase transition from an active phase into infinitely many absorbing states. Examples include the conserved Manna model, the conserved lattice gas, and the conserved threshold transfer process. It is believed that the transitions in these models belong to an autonomous universality class of nonequilibrium phase transitions, the so-called Manna class. Contrarily, the present numerical study of selected (1+1)-dimensional models in this class suggests that their critical behavior converges to directed percolation after very long time, questioning the existence of an independent Manna class.

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“…If one observes universal critical behavior at x c for the CTTP, there might be universality splitting between the CTTP and CLG model on a critical percolation network. The CTTP and CLG model were reported to exhibit different critical behaviors for certain cases, i.e., on a linear chain and on a checkerboard fractal, for which cases the hopping of active particles is deterministic and dominantly deterministic, respectively [23,24].…”

Section: Introductionmentioning

confidence: 99%

Absorbing phase transitions in diluted conserved threshold transfer process

Lee

Kim

2013

Phys. Rev. E

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Absorbing phase transitions in the conserved threshold transfer process (CTTP) on diluted lattices, i.e., on infinite percolation networks, were studied in two dimensions by Monte Carlo simulations. Lattice dilution was found to be irrelevant to the critical behavior for the concentration of diluted sites x far less than the critical concentration x c (=1 − p c , with p c being the percolation threshold), whereas for x close to x c the critical exponents slightly deviated from those of the pure CTTP and new critical exponents were established at x c . The results for x < x c were consistent with the recent results for the conserved lattice gas (CLG) model, whereas the results for x = x c were different from those of the CLG model, for which nonuniversal power-law behavior was observed [Lee, Phys. Rev. E 84, 041123 (2011)]. On the other hand, the critical exponents of the CTTP on a percolation backbone were similar to those on an infinite network and similar to those of the CLG model on a backbone network. The diluted CTTP in three and four dimensions was also investigated, and the critical exponents were similar to those in two dimensions; i.e., the critical exponents were independent of or weakly dependent on the dimensionality. A comment on the recent claim of the absence of a Manna class was also presented.

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Universality split in absorbing phase transition with conserved field on fractal lattices

Cited by 7 publications

References 37 publications

Dependence of asymptotic decay exponents on initial condition and the resulting scaling violation

Dependence of asymptotic decay exponents on initial condition and the resulting scaling violation

Fixed-Energy Sandpiles Belong Generically to Directed Percolation

Absorbing phase transitions in diluted conserved threshold transfer process

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