Nonequilibrium critical behavior in unidirectionally coupled stochastic processes

Phase transitions from an active into an absorbing, inactive state are generically described by the critical exponents of directed percolation (DP), with upper critical dimension [Formula Presented]. In the framework of single-species reaction-diffusion systems, this universality class is realized by the combined processes [Formula Presented] [Formula Presented], and [Formula Presented]. We study a hierarchy of such DP processes for particle species [Formula Presented], unidirectionally coupled via the reactions [Formula Presented] (with rates [Formula Presented]. When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents [Formula Presented] which are markedly reduced at each hierarchy level [Formula Presented]. This scenario can be understood on the basis of the mean-field rate equations, which yield [Formula Presented] at the multicritical point. Using field-theoretic renormalization-group techniques in [Formula Presented] dimensions, we identify a new crossover exponent [Formula Presented], and compute [Formula Presented] in the multicritical regime (for small [Formula Presented] of the second hierarchy level. In the active phase, we calculate the fluctuation correction to the density exponent on the second hierarchy level, [Formula Presented]. Outside the multicritial region, we discuss the crossover to ordinary DP behavior, with the density exponent [Formula Presented]. Monte Carlo simulations are then employed to confirm the crossover scenario, and to determine the values for the new scaling exponents in dimensions [Formula Presented], including the critical initial slip exponent. Our theory is connected to specific classes of growth processes and to certain cellular automata, and the above ideas are also applied to unidirectionally coupled pair annihilation processes. We also discuss some technical as well as conceptual problems of the loop expansion, and suggest some possible interpretations of these difficulties. © 1999 The American Physical Society.