Multicritical behavior in coupled directed percolation processes

We study a hierarchy of directed percolation (DP) processes for particle species A,B,..., unidirectionally coupled via the reactions A --> B,.... When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents beta((k)) which are markedly reduced at each hierarchy level k greater than or equal to 2. We compute the fluctuation corrections to beta((2)) to O(epsilon = 4 - d) using field-theoretic renormalization group techniques. Monte Carlo simulations are employed to determine the new exponents in dimensions d less than or equal to 3.