Novel non-equilibrium critical behavior in unidirectionally coupled stochastic processes

Details Novel non-equilibrium critical behavior in unidirectionally coupled stochastic processes Novel non-equilibrium critical behavior in unidirectionally coupled stochastic processes

1998-09-10

arxiv.org/abs/cond-mat/9809166v2

Phys. Rev. E 59 (1999) 6381

Physics

Condensed Matter

29 pages, 19 figures, revtex, 2 columns, revised Jan 1995: minor changes and additions; accepted for publication in Phys. Rev.

Scientific paper

10.1103/PhysRevE.59.6381

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 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 -> \emptyset. 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 \beta_i which are markedly reduced at each hierarchy level i >= 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. We then include fluctuations by using field-theoretic renormalization group techniques in d = 4-\epsilon dimensions. In the active phase, we calculate the fluctuation correction to the density exponent for the second hierarchy level, \beta_2 = 1/2 - \epsilon/8 + O(\epsilon^2). Monte Carlo simulations are then employed to determine the values for the new scaling exponents in dimensions d<= 3, including the critical initial slip exponent. Our theory is connected to certain classes of growth processes and to certain cellular automata, as well as to unidirectionally coupled pair annihilation processes. We also discuss some technical and conceptual problems of the loop expansion and their possible interpretation.

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