A new class of critical exponents in a dimer-monomer catalytic surface reaction

Yaldram, K.; Khan, K M; Abbasi, Shahab Ahmed; Khan, M.A. Majeed

doi:10.1088/0305-4470/26/17/009

Cited by 25 publications

(32 citation statements)

References 11 publications

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“…Later refined simulations confirmed, however, that the dimer model still belongs to the DP universality class [242]. The same result was found in a similar model for catalysis of dimers and monomers [243,244]. Another important example is the pair contact process without diffusion [245] which is defined by the reaction scheme…”

Section: Dp Models With Infinitely Many Absorbing Statessupporting

confidence: 64%

Non-equilibrium critical phenomena and phase transitions into absorbing states

Hinrichsen¹

2000

Advances in Physics

1,618

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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Section: Dp Models With Infinitely Many Absorbing Statessupporting

confidence: 64%

Non-equilibrium critical phenomena and phase transitions into absorbing states

Hinrichsen¹

2000

Advances in Physics

1,618

193

2,266

View full text Add to dashboard Cite

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“…On the square lattice, the picture is radically different, there being (without diffusion of N), no active stationary state, whatever the value of y [6,[12][13][14]. This observation, based on Monte Carlo simulations, was explained by Brosilow and Ziff (BZ), who argued that the active state is unstable to the filling of one sublattice with N atoms [8].…”

Section: Introductionmentioning

confidence: 99%

Theory of theNO+COsurface-reaction model

et al. 1999

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We derive a pair approximation (PA) for the NO+CO model with instantaneous reactions. For both the triangular and square lattices, the PA, derived here using a simpler approach, yields a phase diagram with an active state for CO-fractions y in the interval y 1 < y < y 2 , with a continuous (discontinuous) phase transition to a poisoned state at y 1 (y 2 ). This is in qualitative agreement with simulation for the triangular lattice, where our theory gives a rather accurate prediction for y 2 . To obtain the correct phase diagram for the square lattice, i.e., no active stationary state, we reformulate the PA using sublattices. The (formerly) active regime is then replaced by a poisoned state with broken symmetry (unequal sublattice coverages), as observed recently by Kortlüke et al. [Chem. Phys. Lett. 275, 85 (1997)]. In contrast with their approach, in which the active state persists, although reduced in extent, we report here the first qualitatively correct theory of the NO+CO model on the square lattice. Surface diffusion of nitrogen can lead to an active state in this case. In one dimension, the PA predicts that diffusion is required for the existence of an active state.

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“…The critical behavior of the continuous transition belongs to the DP universality class when the desorption of adsorbed A is neglected [38,39]. In these investigations, the particle diffusion is neglected.…”

Section: Model and Algorithmmentioning

confidence: 99%

Critical behavior of nonequilibrium continuous phase transition inA+BCcatalytic reaction system

Hua

2004

Phys. Rev. E

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We study two lattice gas models for the A+BC-->AC+ 1/2 B2 reaction system. Model I includes the influences of the adsorbate diffusion and model II includes the effect of the diffusion and position exchange of B and C atoms. Model I exhibits a continuous phase transition with infinitely many absorbing states from a reactive state to a poisoned state of B and C atoms and a discontinuous transition to a poisoned state of A and B atoms when the fraction of A in the gas phase varies. The critical exponents are estimated accurately. The simulation results indicate clearly that the critical behavior of the continuous phase transition in model I belongs to the directed percolation (DP) universality class. Model II, however, exhibits a continuous transition with two absorbing states, and its critical behavior is obviously distinct from the DP universality class.

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A new class of critical exponents in a dimer-monomer catalytic surface reaction

Cited by 25 publications

References 11 publications

Non-equilibrium critical phenomena and phase transitions into absorbing states

Non-equilibrium critical phenomena and phase transitions into absorbing states

Theory of theNO+COsurface-reaction model

Critical behavior of nonequilibrium continuous phase transition inA+BCcatalytic reaction system

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