Multicritical behavior in coupled directed percolation processes

TL;DR

This paper investigates the complex critical behavior of hierarchically coupled directed percolation processes, revealing multicritical phenomena and computing associated critical exponents through theoretical and simulation methods.

Contribution

It introduces a framework for analyzing multicriticality in coupled DP processes and calculates critical exponents using field theory and Monte Carlo simulations.

Findings

Critical exponents decrease at higher hierarchy levels.

Field-theoretic calculations of fluctuation corrections.

Monte Carlo simulations confirm theoretical predictions.

Abstract

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 >= 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 <= 3.