Excluded volume effects in heterogeneous catalysis: reactions between 'dollars' and 'dimes'

Park, Hyunggyu; Köhler, Jutta; Kim, In-Mook; ben‐Avraham, Daniel; Redner, S.

doi:10.1088/0305-4470/26/9/006

Cited by 19 publications

(13 citation statements)

References 12 publications

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“…6). In fact, we have analyzed the P exponent applying the CAM technique to the approximation data and have thus confirmed that the DD model is in the same universality class as Reggeon field theory [19].…”

Section: Of Lr Dirnerssupporting

confidence: 53%

Mean-field (n,m)-cluster approximation for lattice models

1992

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We introduce and study an implementation technique of the mean-field dynamic-cluster method for the analysis of lattice models. The technique is characterized by two indices (n, m), where n is the size of the clusters and m denotes their overlap. For some lattice models, we find that the cluster method converges to the exact kinetics with increasing cluster size n, in a conventional way. However, for some other models it is shown that the cluster approximation predicts a phase diagram that is qualitatively incorrect even for large n. A reason for this anomalous behavior is suggested. The effect of different, but physically equivalent, representations of the same lattice model on the quality of the approximation results is also explored.PACS number(s): 05.40. +j, 64.60.Ht, 82.20. Mj, 82.65.Jv

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Section: Of Lr Dirnerssupporting

confidence: 53%

Mean-field (n,m)-cluster approximation for lattice models

1992

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“…From Eqs. (4) and (6), it follows that for small x the curve converges to a constant value, while for large x it should follow a straight line with slope p. We find that the data for the various system sizes are best collapsed to a curve with choices p, = 0.5815 (5) does not involve the dynamical processes with the mass conservation of modulo 2. Nevertheless, the values of the critical exponents are clearly different from the DP values and seem to be consistent with the values of the PCA and the BAW, in which the mass conservation of modulo 2 governs the dynamics.…”

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confidence: 74%

“…Recently, an interacting monomer-monomer model [6,7] has been introduced where particles of the same species have variable repulsive interactions. When the interaction strength is weak, the interaction model exhibits only a first-order phase transition between two saturated phases.…”

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confidence: 99%

Critical Behavior of an Interacting Monomer-Dimer Model

1994

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We study a monomer-dimer model with repulsive interactions between the same species in one dimension. With infinitely strong interactions the model exhibits a continuous transition from a reactive phase to an inactive phase with two equivalent absorbing states. Monte Carlo simulations show that the critical behavior is different from the conventional directed percolation universality class but seems to be consistent with that of the models with the mass conservation of modulo 2.

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“…In fact, DP seems to be even more general and may be identified in systems that violate some of the four conditions, for example in certain models with nonunique [146][147][148][149] or fluctuating passive states [129]. Even complicated spreading processes with several spreading agents and multicomponent order parameters were shown to exhibit DP behavior [122,124,146,[150][151][152][153]. Some models with infinitely many absorbing states, that were initially thought to belong to different universality classes, were later found to be in the DP class as well (see Sec.…”

Section: Phenomenological Scaling Theorymentioning

confidence: 99%

Non-equilibrium critical phenomena and phase transitions into absorbing states

Hinrichsen¹

2000

Advances in Physics

1,595

193

2,266

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This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, fieldtheoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic nonequilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.

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Excluded volume effects in heterogeneous catalysis: reactions between 'dollars' and 'dimes'

Cited by 19 publications

References 12 publications

Mean-field (n,m)-cluster approximation for lattice models

Mean-field (n,m)-cluster approximation for lattice models

Critical Behavior of an Interacting Monomer-Dimer Model

Non-equilibrium critical phenomena and phase transitions into absorbing states

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