One-dimensional lattice gas models with infinitely many absorbing states

Fiore, Carlos E.; Oliveira, Mário J. de

doi:10.1590/s0103-97332006000200014

Cited by 5 publications

(5 citation statements)

References 6 publications

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“…9(d), gives z = 1.50(2) and β/ν ⊥ = 0.251 (4). A summary of these critical exponents can be found in Table II, along with the results of previous studies of CLG on a ladder and a modified version of CLG in one dimension studied by Fiore and Oliveira [28], where both adjacent active particles may jump simultaneously to their respective neighboring vacant sites.…”

Section: Conserved Lattice Gas (Clg)mentioning

confidence: 94%

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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Section: Conserved Lattice Gas (Clg)mentioning

confidence: 94%

Fixed-Energy Sandpiles Belong Generically to Directed Percolation

et al. 2012

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“…The one-dimensional CLG, which is the symmetric version of a special case µ = 1 of RASEP, also flows to DP when density conservation is broken. In a recent work, Fiore et al [21] have claimed that a modified CLG, which includes next nearest neighbour interaction and simultaneous jump of two consecutive particles in opposite direction but does not violate particle conservation, shows nontrivial critical behaviour. It still remains to see whether it is possible to modify the dynamics of RASEP in a different way, keeping density conservation, to obtain the DP critical behaviour.…”

Section: -P4mentioning

confidence: 99%

“…al. [20] have claimed that a modified CLG, which includes next nearest neighbour interaction and simultaneous jump of two consecutive particles in opposite direction but does not violate particle conservation, shows non-…”

mentioning

confidence: 99%

Restricted exclusion processes without particle conservation flows to directed percolation

Basu¹,

Mohanty²

2012

EPL

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Absorbing phase transition in restricted exclusion processes are characterized by simple integer exponents. We show that this critical behaviour flows to the directed percolation (DP) universality class when particle conservation is broken suitably. The same transition, when studied using the average density as the controlling parameter, yields critical exponents quite different from DP; we argue that these exponents are actually related to DP by a scaling factor 1/βDP . These conclusions also apply to conserved lattice gas in one dimension.

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“…Differently from the continuous case, one-dimensional discontinuous absorbing transitions has been much less observed. Except in special cases [8][9][10], its manifestation in short range systems have been the subject of a longstanding controversy [11][12][13][14][15]. The absence of a discontinuous transition would stem from the suppression of compact clusters coming from the large fluctuations in one dimension.…”

Section: Introductionmentioning

confidence: 99%

Robustness of first-order phase transitions in one-dimensional long-range contact processes

Fiore

Oliveira

2013

Phys. Rev. E

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It has been proposed (Phys. Rev. E 71, 026121 (2005)) that unlike the short range contact process, a long-range counterpart may lead to the existence a discontinuous phase transition in one dimension. Aiming at exploring such link, here we investigate thoroughly a family of longrange contact processes. They are introduced through the transition rate 1 + aℓ −σ , where ℓ is the length of inactive islands surrounding particles. In the former approach we reconsider the original model (called σ−contact process), by considering distinct mechanisms of weakening the long-range interaction toward the short-range limit. Second, we study the effect of different rules, including creation and annihilation by clusters of particles and distinct versions with infinitely many absorbing states. Our results show that all examples presenting a single absorbing state, a discontinuous transition is possible for small σ. On the other hand, the presence of infinite absorbing states leads to distinct scenario depending on the interactions at the frontier of inactive sites.

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One-dimensional lattice gas models with infinitely many absorbing states

Cited by 5 publications

References 6 publications

Fixed-Energy Sandpiles Belong Generically to Directed Percolation

Fixed-Energy Sandpiles Belong Generically to Directed Percolation

Restricted exclusion processes without particle conservation flows to directed percolation

Robustness of first-order phase transitions in one-dimensional long-range contact processes

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