Generalized scaling relations for unidirectionally coupled nonequilibrium systems

TL;DR

This paper investigates unidirectionally coupled nonequilibrium systems at multicritical points, revealing inhomogeneous active regions and deriving generalized scaling relations confirmed through numerical simulations.

Contribution

It introduces generalized scaling relations for unidirectionally coupled systems at multicritical points, supported by numerical validation.

Findings

Inhomogeneous active regions are a common feature in such systems.

Particle number grows algebraically with different exponents in coupled and uncoupled domains.

Derived hyperscaling relations are confirmed numerically for DP and PC class models.

Abstract

Unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point. We find that for initial conditions with isolated particles, each hierarchy level exhibits an inhomogeneous active region, coupled and uncoupled respectively. The particle number of each level increases algebraically in time as $N(t) \sim t^{\eta}$ with different exponents $\eta$ in each domain. This inhomogeneity is a quite general feature of unidirectionally coupled systems and leads to two hyperscaling relations between dynamic and static critical exponents. Using the contact process and the branching-annihilating random walk with two offsprings, which belong to the DP and PC classes respectively, we numerically confirm the scaling relations.