Wilson renormalization of a reaction–diffusion process

Wijland, Frédéric van; Oerding, K.; Hilhorst, H. J.

doi:10.1016/s0378-4371(97)00603-1

Cited by 136 publications

(212 citation statements)

References 18 publications

(38 reference statements)

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“…For example in a similar model that exhibits an additional global particle number conservation [8] such situation was found. Therefore I investigated by extensive simulations this question.…”

Section: Cluster Mean-field Results For Pcpdmentioning

confidence: 83%

Critical behavior of the one-dimensional diffusive pair contact process

Ódor

2003

Phys. Rev. E

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The phase transition of the one-dimensional, diffusive pair contact process (PCPD) is investigated by N cluster mean-field approximations and high precision simulations. The N = 3, 4 cluster approximations exhibit smooth transition line to absorbing state by varying the diffusion rate D with β2 = 2 mean-field order parameter exponent of the pair density. This contradicts with former N = 2 results, where two different mean-field behavior was found along the transition line. Extensive dynamical simulations on L = 10 5 lattices give estimates for the order parameter exponents of the particles for 0.05 ≤ D ≤ 0.7. These data can support former two distinct class findings. However the gap between low and high D exponents is narrower than estimated previously and the possibility for interpreting numerical data as a single class behavior with exponents α = 0.21(1), β = 0.41(1) assuming logarithmic corrections is shown. Finite size scaling and cluster simulation results are also presented.

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Section: Cluster Mean-field Results For Pcpdmentioning

confidence: 83%

Critical behavior of the one-dimensional diffusive pair contact process

Ódor

2003

Phys. Rev. E

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“…According to the analogy discussed above one expects the following scaling form for the two-time response function in momentum space (see, e.g., [2,28] and section 3 in [27])…”

Section: Scaling Formsmentioning

confidence: 98%

“…In both cases the order parameter m(t) := ϕ(x, t) ‡ § provides a background for the fluctuations, with a universal scaling behavior [28,29] …”

Section: Scaling Formsmentioning

confidence: 99%

“…In both cases it turns out that the width ∆ 0 = [ϕ(x, 0) − m 0 ] 2 of the initial distribution of the order parameter ϕ -assumed with short-ranged spatial correlations -is irrelevant [29,28] and controls only corrections to the leading scaling behavior, so that an initial state with ∆ 0 = 0 is asymptotically equivalent to one with no fluctuations ∆ 0 = 0. Equation (9) clearly shows that a non-vanishing value of the initial order parameter introduces an additional time scale in the problem…”

Section: Scaling Formsmentioning

confidence: 99%

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Ageing in the contact process: scaling behaviour and universal features

Baumann

Gambassi

2007

J. Stat. Mech.

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Abstract. We investigate some aspects of the ageing behavior observed in the contact process after a quench from its active phase to the critical point. In particular we discuss the scaling properties of the two-time response function and we calculate it and its universal ratio to the two-time correlation function up to first order in the field-theoretical ǫ-expansion (ǫ = 4 − d). The scaling form of the response function does not fit the prediction of the theory of local scale invariance. Our findings are in good qualitative agreement with recent numerical results. ‡ Laboratoire associé au CNRS UMR 7556

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“…For example, we have seen that the directed percolation universality class quite generically describes the critical properties of phase transitions from active to inactive, absorbing states, which abound in nature. The few exceptions to this rule either require the coupling to another conserved mode [83,84]; the presence, on a mesoscopic level, of additional symmetries that preclude the spontaneous decay A → ∅ as in the so-called parity-conserving (PC) universality class, represented by branching and annihilating random walks A → (n + 1) A with n even, and A + A → ∅ [85] (for recent developments based on nonperturbative RG approaches, see Ref. [86]); or the absence of any first-order reactions, as in the (by now rather notorious) pair contact process with diffusion (PCPD) [87], which has so far eluded a successful field-theoretic treatment [88].…”

Section: Discussionmentioning

confidence: 99%

Field-Theory Approaches to Nonequilibrium Dynamics

Täuber

Ageing and the Glass Transition

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It is explained how field-theoretic methods and the dynamic renormalisation group (RG) can be applied to study the universal scaling properties of systems that either undergo a continuous phase transition or display generic scale invariance, both near and far from thermal equilibrium. Part 1 introduces the response functional field theory representation of (nonlinear) Langevin equations. The RG is employed to compute the scaling exponents for several universality classes governing the critical dynamics near second-order phase transitions in equilibrium. The effects of reversible mode-coupling terms, quenching from random initial conditions to the critical point, and violating the detailed balance constraints are briefly discussed. It is shown how the same formalism can be applied to nonequilibrium systems such as driven diffusive lattice gases. Part 2 describes how the master equation for stochastic particle reaction processes can be mapped onto a field theory action. The RG is then used to analyse simple diffusion-limited annihilation reactions as well as generic continuous transitions from active to inactive, absorbing states, which are characterised by the power laws of (critical) directed percolation. Certain other important universality classes are mentioned, and some open issues are listed.

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Wilson renormalization of a reaction–diffusion process

Cited by 136 publications

References 18 publications

Critical behavior of the one-dimensional diffusive pair contact process

Critical behavior of the one-dimensional diffusive pair contact process

Ageing in the contact process: scaling behaviour and universal features

Field-Theory Approaches to Nonequilibrium Dynamics

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