The phase transition of the diffusive pair contact process revisited

Abstract

The restricted diffusive pair contact process 2A->3A, 2A->0 (PCPD) and the classification of its critical behavior continues to be a challenging open problem of non-equilibrium statistical mechanics. Recently Kockelkoren and Chate [Phys. Rev. Lett. 90, 125701 (2003)] suggested that the PCPD in one spatial dimension represents a genuine universality class of non-equilibrium phase transitions which differs from previously known classes. To this end they introduced an efficient lattice model in which the number of particles per site is unrestricted. In numerical simulations this model displayed clean power laws, indicating ordinary critical behavior associated with certain non-trivial critical exponents. In the present work, however, we arrive at a different conclusion. Increasing the numerical effort, we find a slow drift of the effective exponents which is of the same type as observed in previously studied fermionic realizations. Analyzing this drift we discuss the possibility that the asymptotic critical behavior of the PCPD may be governed by an ordinary directed percolation fixed point.Comment: 6 pages, 1 figur

A class of exactly solved assisted-hopping models of active-inactive state transition on a line

“…Introduction -There has recently been a lot of interest in models showing an active-absorbing state transition [1][2][3]. The best studied of these is the directed percolation (DP) class [4,5], and the related pair-contact process with diffusion (PCPD) [6][7][8] and parity-conserving directed percolation (PC) [9,10]. Models with conserved number of particles where a particle may hop only if there are sufficient number of other particles present within a given range, also show an active-absorbing phase transition, where the lowdensity phase is inactive.…”

Nonequilibrium phase transitions into absorbing states

“…For the one dimensional PCPD, however, the numerically estimated critical exponents of the PCPD are so similar to those of the DP that the possibility for the PCPD to belong to the DP class has been raised [36,37]. Interestingly, the critical exponent 6 δ which describes the density decay with time at criticality has floated from ≃ 0.28 [38] to less than 0.185 [37] with time, which is due to the strong corrections to scaling.…”

“…Interestingly, the critical exponent 6 δ which describes the density decay with time at criticality has floated from ≃ 0.28 [38] to less than 0.185 [37] with time, which is due to the strong corrections to scaling. For comparison, the numerical value of δ DP is ≃ 0.15946 [39].…”

“…An argument in favor of the DP scenario was suggested by Hinrichsen [37]. The starting point of the argument is the numerical observation that the dynamic exponent z is smaller than 2 which is the dynamic exponent of the random walk.…”

Out-of-equilibrium stationary states, percolation, and subcritical instabilities in a fully nonconservative system

“…In that version, our model has a true absorbing phase and is very close to the pair contact process with diffusion (PCPD). The PCPD model has two states [6,[21][22][23], one is an absorbing phase where at most one particle diffuses. The second one is made of patches of persistent activity.…”