Influence of turbulent mixing on critical behavior of directed percolation process: Effect of compressibility

Universal behavior is a typical emergent feature of critical systems. A paramount model of the nonequilibrium critical behavior is the directed bond percolation process that exhibits an active-to-absorbing state phase transition in the vicinity of a percolation threshold. Fluctuations of the ambient environment might affect or destroy the universality properties completely. In this work, we assume that the random environment can be described by means of compressible velocity fluctuations. Using field-theoretic models and renormalization group methods, we investigate large-scale and long-time behavior. Altogether, 11 universality classes are found, out of which 4 are stable in the infrared limit and thus macroscopically accessible. In contrast to the model without velocity fluctuations, a possible candidate for a realistic three-dimensional case, a regime with relevant short-range noise, is identified. Depending on the dimensionality of space and the structure of the turbulent flow, we calculate critical exponents of the directed percolation process. In the limit of the purely transversal random force, critical exponents comply with the incompressible results obtained by previous authors. We have found intriguing nonuniversal behavior related to the mutual effect of compressibility and advection. © 2018 American Physical Society