2012/02/29 by Su-Chan Park, Su‐Chan Park
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Critical exponent #Crossover #Diffusion #Directed percolation #Discontinuity (linguistics) #Exponent #Geometry #Material Dynamics and Properties #Mathematical analysis #Mathematics #Monte Carlo method #Percolation (cognitive psychology) #Phase transition #Physics #Scaling #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.90.052115
published as Phys. Rev. E 90, 052115 (2014) · 11 pages, 12 figures, published
openalex publication_date 2014/11/11 · arxiv created 2014/11/21 · arxiv updated 2014/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the one-dimensional pair contact process with diffusion (PCPD) by extensive Monte Carlo simulations, mainly focusing on the critical density decay exponent δ. To obtain an accurate estimate of δ, we first find the strength of corrections to scaling using the recently introduced method [S.-C. Park. J. Korean Phys. Soc. 62, 469 (2013)KPSJAS0374-488410.3938/jkps.62.469]. For small diffusion rate (d≤0.5), the leading corrections-to-scaling term is found to be ∼t-0.15, whereas for large diffusion rate (d=0.95) it is found to be ∼t-0.5. After finding the strength of corrections to scaling, effective exponents are systematically analyzed to conclude that the value of critical decay exponent δ is 0.173(3) irrespective of d. This value should be compared with the critical decay exponent of the directed percolation, 0.1595. In addition, we study two types of crossover. At d=0, the phase boundary is discontinuous and the crossover from the pair contact process to the PCPD is found to be described by the crossover exponent ϕ=2.6(1). We claim that the discontinuity of the phase boundary cannot be consistent with the theoretical argument supporting the hypothesis that the PCPD should belong to the DP. At d=1, the crossover from the mean field PCPD to the PCPD is described by ϕ=2 which is argued to be exact.