Absorbing-state critical phenomena in interacting surface reaction models

Abstract

Absorbing-state critical phenomena in various surface reaction models are brie y reviewed, focusing on their universal properties. The directed percolation universality class and the directed Ising universality class are identi ed, associated with absorbing-state phase transitions in these onedimensional reaction models. I IntroductionDuring the last decades, nonequilibrium critical phenomena have been extensively studied in various areas such as epidemiology, biology, c hemistry, sociology and physics 1-4 . An interesting example of nonequilibrium phase transitions is the absorbing phase transition. In this case, there exist some absorbing trapped states in con gurational phase space. If the system gets into one of these absorbing states by the evolution dynamics, then the system is trapped: no further dynamics can occur, to escape from the absorbing state. By controlling an external parameter, the system may undergo a continuous phase transition from an active steady-state phase into an inactive absorbing phase. In the active phase, the system manages to avoid the traps so it has a nite probability to stay alive forever.Recently, v arious kinds of nonequilibrium lattice models exhibiting absorbing transitions have been studied extensively 3-6 . These models describe a wide range of phenomena, in particular, epidemic spreading, catalytic chemical reactions, and transport in disordered media. Two distinct types of absorbing phase transitions have been identi ed in one dimension: the directed percolation DP and directed Ising DI universality class. Most models have been found to belong to the DP class 7-13 , which i n volves typically a single absorbing state or multiple absorbing states with one of them dynamically more prominent than the others no explicit symmetry. DI type critical behavior appears in models with two equivalent absorbing states or two equivalent classes of absorbing states Ising type symmetry 14-21 . The degeneracy of the absorbing states may be obscured by an alternative representation of the models. By assigning kinks or particles between di erent absorbing domains, the multiple absorbing states correspond to a single vacuum con guration and their degeneracy translates into particlenumber conservation. For example, in the dynamics of branching annihilating random walks BAW 22-25 , the vacuum absorbing state is not degenerate, but the absorbing transition belongs to the DI class if the dynamics conserve the particle number modulo 2. So the DI class is sometimes called the PC parity-conserving universality class.In this paper, we focus on nonequibirium surface reaction models exhibiting absorbing transitions. In Sec. II, we discuss the universality classes for various noninteracting surface reaction models. In Sec. III, the surface reaction models with lateral interactions are discussed. Finally, w e summarize our discussions.II Noninteracting surface reaction models Monomer-dimer model In 1986, Zi , Gulari and Barshad introduced a monomer-dimerMD model to describe the oxidation of carbon m...