Generalized scaling relations for unidirectionally coupled nonequilibrium systems

2003/12/04 by Sungchul Kwon, Gunter M. Schütz, Gunter M. Schutz
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Geometry #Mathematics #Non-equilibrium thermodynamics #Physics #Scaling #Spectroscopy and Quantum Chemical Studies #Statistical physics #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech

paper · pdf · doi:10.1016/j.physa.2004.04.111

4 pages, 3 figures, 1 table

arxiv created 2003/12/04 · openalex publication_date 2004/06/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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) ∼ t^η with different exponents η 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.

Citations

• Stochastic Lattice Models with Several Absorbing States
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