Critical behaviour for mixed site-bond directed percolation

Abstract

We study mixed site-bond directed percolation on 2D and 3D lattices by using time-dependent simulations. Our results are compared with rigorous bounds recently obtained by Liggett and by Katori and Tsukahara.The critical fractions p c site and p c bond of sites and bonds are extremely well approximated by a relationship reported earlier for isotropic percolation,

An Investigation of Site-Bond Percolation on Many Lattices

“…3. The fits to the scaling relation (8) yield values for γ that are consistent with the literature values. The strength P of the infinite cluster scales as…”

Universal scaling behaviour of directed percolation and the pair contact process in an external field

“…The order parameter and its fluctuations as a function of the external field h are presented in figure 5. Approaching the transition point, ρ a and ∆ρ a scale according to the equations (6,7) where the exponents β/σ and γ ′ /σ agree with the DP values.…”

“…The field dependence of the order parameter and its fluctuations (inset) at the critical value pc for the pair contact process. The dashed lines correspond to the expected power-law behavior(6,7).…”

Yang$ndash$Lee zeros for a nonequilibrium phase transition

“…where x is the position and z = ν || /ν ⊥ is the so-called dynamic exponent. Numerical estimates for the values of p c and the critical exponents in 1+1 dimensions are p c = 0.6447001(1), β = 0.27649(4), ν ⊥ = 1.096844 (14) and ν || = 1.733825(15) [11] (bond percolation) and p c = 0.705489(4) [12] (site percolation). Although DP can be defined and easily simulated, it is one of the very few systems for which -even in one spatial dimension -no analytical solution is known, suggesting that DP is a non-integrable process.…”