The dimer-trimer model for heterogeneous catalysis: a new universality class

Köhler, Jutta; ben‐Avraham, Daniel

doi:10.1088/0305-4470/24/11/009

Cited by 56 publications

(51 citation statements)

References 12 publications

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“…Note also that the branching of a pair induces effective diffusion for the B's. A large number of systems, such as the dimer reaction [11], the dimer-dimer [25] and dimer-trimer [26] reactions, or the threshold transfer process [27] are modeled by the above mechanism.…”

Section: Pair Contact Process (Pcp)mentioning

confidence: 99%

Infinitely-many absorbing-state nonequilibrium phase transitions

Wijland¹

2003

Braz. J. Phys.

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We present a general field-theoretic strategy to analyze three connected families of continuous phase transitions which occur in nonequilibrium steady-states. We focus on transitions taking place between an active state and one absorbing state, when there exist an infinite number of such absorbing states. In such transitions the order parameter is coupled to an auxiliary field. Three situations arise according to whether the auxiliary field is diffusive and conserved, static and conserved, or finally static and not conserved. I The ubiquity of absorbing-state transitionsThis overview is devoted to a study of nonequilibrium phase transitions taking place between the active and the absorbing state of a system, as some control parameter is varied across a threshold value. Such transitions are encountered in a variety of fields ranging from chemical kinetics to the spreading of computer viruses [1]. From a theoretical standpoint absorbing state transitions form natural counterparts to equilibrium phase transitions. The transition rates used in the stochastic dynamics employed to model the physical phenomenon under consideration do not satisfy detailed balance (with respect to an a priori defined energy function). In spite of this apparent freedom, the number of universality classes that the transition can fall into is incredibly small. Among known universality classes, that of directed percolation (DP) is by far the broadest. And indeed, in the absence of additional symmetries or conservation laws, as was conjectured twenty years ago by Grassberger [2], an absorbing state transition will invariably fall into the DP universality class. The interest in absorbing state transitions was further enhanced as Dickman and coworkers [3] established a one-to-one correspondence with self-organized critical systems (see [4] for a review on self-organized criticality). They were able to show that the scaling behavior observed there was entirely governed by an underlying nonequilibrium phase transition (which, as a side effect, somewhat tempers the mystics of SOC). The study of exactly which microscopic ingredients make an absorbing state transition not belong to the DP class has almost grown into a field of its own. It was early realized that if the microscopic dynamics possesses additional conservation laws the universality class of the transition could be different. Discrete conservation laws, such as the conservation of the parity of the number of particles [5], are known to be driving the transition to an independent universality class (the Parity Conserving or Voter class [6]). A recent study attempts to provide a comprehensive table of all possible transitions involving the dynamics of a single field [7]. Besides, the effect of a continuous symmetry was shown either to change the universality class of the transition [8,9] or to simply destroy its continuous nature [10]. The continuous symmetry present in the systems studied there arose from a local conservation law.An independent direction of research has focused on absorbi...

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Section: Pair Contact Process (Pcp)mentioning

confidence: 99%

Infinitely-many absorbing-state nonequilibrium phase transitions

Wijland¹

2003

Braz. J. Phys.

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“…Our guess is that a Reggeon field theory [11,10] with a spatio-temporal dependent anisotropic Laplacian term (which, for example, would enhance, un-favor or forbid diffusion from certain sites in certain directions) could be a good candidate to describe this new phenomenology. Analogously to what happens in field theoretical descriptions of other systems with many a absorbing states [13,24], the inhomogeneous Laplacian-term coefficient should be described by a second physical field coupled to the activity field in such a way that its fluctuations would vanish upon local absence of activity. Further pursuing this line of reasoning is beyond the scope of the present paper.…”

Section: Discussionmentioning

confidence: 99%

“…Two possible follow-ups of this work are: (1) It would be worth studying in more realistic situations as, for instance, in surface catalysis (dimer-dimer or dimer-trimer) models [13] whether effects similar to those described in this paper play any relevant role. In particular, for those models depending upon lattice and particle geometry there are cases in which activity cannot propagate to neighboring regions, but is constrained to evolve following certain directions or paths.…”

Section: Discussionmentioning

confidence: 99%

“…In particular, for those models depending upon lattice and particle geometry there are cases in which activity cannot propagate to neighboring regions, but is constrained to evolve following certain directions or paths. It would be rather interesting to sort out whether anomalies reported for those models [13] transitions, and would permit to shed some light on the degree of universality of this anomalous phenomenology. Our guess is that a Reggeon field theory [11,10] with a spatio-temporal dependent anisotropic Laplacian term (which, for example, would enhance, un-favor or forbid diffusion from certain sites in certain directions) could be a good candidate to describe this new phenomenology.…”

Section: Discussionmentioning

confidence: 99%

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Systems with superabsorbing states

Hurtado

Muñoz

2000

Phys. Rev. E

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We report on some extensive analysis of a recently proposed model [A. Lipowski Phys. Rev. E 60, 6255 (1999)] with infinitely many absorbing states. By performing extensive Monte Carlo simulations we have determined critical exponents and show strong evidence that this model is not in the directed percolation universality class. The conjecture that this two-dimensional model exhibits a dimensional reduction (behaving as one-dimensional directed percolation) is firmly disproven. The reason for the model not exhibiting standard directed percolation scaling behavior is traced back to the existence of what we call superabsorbing sites, i.e. absorbing sites that cannot be directly activated by the presence of neighboring activity in one or more than one directions. Supporting this claim we present two strong evidences: (i) in one dimension, where superabsorbing sites do not appear at the critical point, the system behaves as directed percolation, and (ii) in a modified two-dimensional variation of the model, defined on a honeycomb lattice, for which superabsorbing sites are very rarely observed, directed percolation behavior is recovered. Finally, a parallel updating version of the model exhibiting a nonequilibrium first-order transition is also reported.

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“…For example, Schl6gl's so-called "first model" (Schl6gl 1972) describes the reactions X ~ 2X and X @ 0. 4 If the rate of the reaction 0 --* X, wherein X is produced spontaneously from the vacuum (i.e., 0), is zero, then the vacuum state with no X's 4 Other models of catalytic reactions exhibiting an absorbing state can be found in Kohler & ben-Avraham (1991) and ben-Avraham & Kohler (1992).…”

Section: Directed Percolation and Related Problemsmentioning

confidence: 99%