2007/01/15 by Sungchul Kwon, Kwon, Sungchul, Yup Kim +1
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0701315
5 pages and 5 figures
openalex publication_date 2007/01/15 · arxiv created 2007/01/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the domain structure of pair contact process with diffusion (PCPD). PCPD is a stochastic reaction-diffusion model which evolves by the competition of two binary reactions, 2A → 3A and 2A → 0. In addition, each particle diffuses isotropically, which leads to the bidirectional coupling between solitary particles and pairs. The coupling from pairs to solitary particles is linear, while the opposite coupling is quadratic. The spreading domain formed from localized activities in vacuum consists of two regions, the coupled region of size Rp where pairs and solitary particles coexist and the uncoupled region of size RU where only solitary particles exist respectively. As the size of the whole domain R is given as R=Rp + RU, Rp and RU are the basic length scales of PCPD. At criticality, Rp and RU scale as Rp ∼ t1/Zp and RU ∼ t1/ZU with ZU > Zp. We estimate Zp =1.61(1) and ZU =1.768(8). Hence, the correction to the scaling of R, Q=RU /Rp extremely slowly decays, which makes it practically impossible to identify the asymptotic scaling behavior of R. In addition to the generic feature of the bidirectional coupling, the double domain structure is another reason for the extremely slow approach to the asymptotic scaling regime of PCPD.