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 β⁽ᵏ⁾ which are markedly reduced at each hierarchy level k≥2. We compute the fluctuation corrections to β⁽²⁾ to O(ε0ex0ex=0ex0ex4-d) using field-theoretic renormalization group techniques. Monte Carlo simulations are employed to determine the new exponents in dimensions d≤3.
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Täuber et al. (1998) studied this question.
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