Nonequilibrium critical behavior in unidirectionally coupled stochastic processes

Phase transitions from an active into an absorbing, inactive state an generically described by the critical exponents of directed percolation (DP), with upper critical dimension d(c)= 4. In the framework of single-species reaction-diffusion systems, this universality class is realized by the combined processes A-->A +A, A +A -->A, and A-->0. We study a hierarchy of such DP processes for particle species A,B,..., unidirectionally coupled via the reactions A-->B,... (with rates mu(AB),,,...). When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents Pi which are markedly reduced at each hierarchy level i greater than or equal to 2. This scenario can be understood on the basis of the mean-field rate equations, which yield beta(i),= 1/2(i-1) at the multicritical point. Using field-theoretic renormalization-group techniques in d=4-is an element of dimensions, we identify a new crossover exponent phi, and compute phi = 1+ O(is an element of(2)) in the multicritical regime (for small mu(AB),,) of the second hierarchy level. In the active phase, we calculate the fluctuation correction to the density exponent on the second hierarchy level, beta(2)= 1/2- is an element of/8 O(,is an element of(2)). Outside the multicritial region, we discuss the crossover to ordinary DP behavior, with the density exponent beta(1),= 1 - is an element of/6+ O(is an element of(2)). Monte Carlo simulations are then employed to confirm the crossover scenario, and to determine the values for the new scaling exponents in dimensions d less than or equal to 3, 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. [S1063-651X(99)02906-2].