Moment ratios for the pair-contact process with diffusion

2006/05/26 by Marcelo Martins de Oliveira, Marcelo M. de Oliveira, Ronald Dickman
Materials Science · Mathematics · Physics and Astronomy · #Computer science #Condensed matter physics #Contact process (mathematics) #Critical exponent #Critical point (mathematics) #Diffusion #Directed percolation #Geometry #Material Dynamics and Properties #Mathematical analysis #Mathematics #Moment (physics) #Order (exchange) #Percolation (cognitive psychology) #Percolation threshold #Phase transition #Physics #Point (geometry) #Point process #Process (computing) #Quantum mechanics #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.74.011124

17 pages, 5 figures

arxiv created 2006/05/26 · openalex publication_date 2006/07/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the continuous absorbing-state phase transition in the one-dimensional pair contact process with diffusion (PCPD). In previous studies [Dickman and de Menezes, Phys. Rev. E 66, 045101(R) (2002)], the critical point moment ratios of the order parameter showed anomalous behavior, growing with system size rather than taking universal values, as expected. Using the quasistationary simulation method we determine the moments of the order parameter up to fourth order at the critical point, in systems of up to 40,960 sites. Due to strong finite-size effects, the ratios converge only for large system sizes. Moment ratios and associated order-parameter histograms are compared with those of directed percolation. We also report an improved estimate [pc=0.077092(1)] for the location of the critical point in the nondiffusive pair contact process.

Citations

• Critical behavior of the one-dimensional annihilation-fission process2A→Ø,2A→3A
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