The non-equilibrium phase transition of the pair-contact process with diffusion

Henkel, Malte; Hinrichsen, Haye

doi:10.1088/0305-4470/37/28/r01

Cited by 87 publications

(111 citation statements)

References 96 publications

(319 reference statements)

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“…1,2 For non-equilibrium systems where the rates for transitions between states do not satisfy detailed-balance, there is even less understanding regarding fundamental behavior given the lack of a thermodynamic free energy framework. 3,4 Characterizing behavior in these systems has been presented as a "scientific grand challenge." 5 In particular, the lack of applicability of the Gibbs phase rule opens the possibility for phase coexistence in a finite region of parameter space with non-zero "volume" (i.e., for finite range of a single control parameter or in a region with nonzero area rather than just along a curve in a two-dimensional parameter space).…”

Section: Introductionmentioning

confidence: 99%

Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Wang

Liu

Evans

2015

The Journal of Chemical Physics

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Threshold versions of Schloegl's model on a lattice, which involve autocatalytic creation and spontaneous annihilation of particles, can provide a simple prototype for discontinuous non-equilibrium phase transitions. These models are equivalent to so-called threshold contact processes. A discontinuous transition between populated and vacuum states can occur selecting a threshold of N ≥ 2 for the minimum number, N, of neighboring particles enabling autocatalytic creation at an empty site. Fundamental open questions remain given the lack of a thermodynamic framework for analysis. For a square lattice with N = 2, we show that phase coexistence occurs not at a unique value but for a finite range of particle annihilation rate (the natural control parameter). This generic two-phase coexistence also persists when perturbing the model to allow spontaneous particle creation. Such behavior contrasts both the Gibbs phase rule for thermodynamic systems and also previous analysis for this model. We find metastability near the transition corresponding to a non-zero effective line tension, also contrasting previously suggested critical behavior. Mean-field type analysis, extended to treat spatially heterogeneous states, further elucidates model behavior. Keywordsphysical chemistry, annihilation rates, control parameters, discontinuous transition, nonequilibrium phase transitions, particle creation, phase co-existence, thermodynamic framework Threshold versions of Schloegl's model on a lattice, which involve autocatalytic creation and spontaneous annihilation of particles, can provide a simple prototype for discontinuous non-equilibrium phase transitions. These models are equivalent to so-called threshold contact processes. A discontinuous transition between populated and vacuum states can occur selecting a threshold of N ≥ 2 for the minimum number, N, of neighboring particles enabling autocatalytic creation at an empty site. Fundamental open questions remain given the lack of a thermodynamic framework for analysis. For a square lattice with N = 2, we show that phase coexistence occurs not at a unique value but for a finite range of particle annihilation rate (the natural control parameter). This generic two-phase coexistence also persists when perturbing the model to allow spontaneous particle creation. Such behavior contrasts both the Gibbs phase rule for thermodynamic systems and also previous analysis for this model. We find metastability near the transition corresponding to a non-zero effective line tension, also contrasting previously suggested critical behavior. Mean-field type analysis, extended to treat spatially heterogeneous states, further elucidates model behavior. C 2015 AIP Publishing LLC. [http://dx

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Section: Introductionmentioning

confidence: 99%

Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Wang

Liu

Evans

2015

The Journal of Chemical Physics

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“…It almost constitutes a euphemism to state that this and the subsequent flurry of numerical work [9][10][11][12][13][14][15][16][17][18][19] have revealed conflicting views (see Ref. [20] for a comprehensive overview), for not only are the precise numerical values of the critical exponents still being debated to this day, but even more striking, the very issue of the PCPD universality class has remained controversial. Essentially three scenarios have been put forward: Either the transition defines a novel independent universality class that is yet to be characterized, or it belongs to the CP/DP, or even to the PC class (the latter perhaps becoming less likely with improving simulation accuracy).…”

Section: Introductionmentioning

confidence: 99%

Pair contact process with diffusion: Failure of master equation field theory

et al. 2004

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We demonstrate that the "microscopic" field theory representation, directly derived from the corresponding master equation, fails to adequately capture the continuous nonequilibrium phase transition of the pair contact process with diffusion (PCPD). The ensuing renormalization group (RG) flow equations do not allow for a stable fixed point in the parameter region that is accessible by the physical initial conditions. There exists a stable RG fixed point outside this regime, but the resulting scaling exponents, in conjunction with the predicted particle anticorrelations at the critical point, would be in contradiction with the positivity of the equal-time mean-square particle number fluctuations. We conclude that a more coarse-grained effective field theory approach is required to elucidate the critical properties of the PCPD.

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“…The mean field critical exponents are β = 1 and δ = β/ν = 1 2 [33,34], which are different from those of DP (β = ν = 1) [2]. Since the upper critical dimension of the PCPD is believed to be 2 [35], for most physically relevant cases (d ≥ 2) the PCPD does not belong to the DP class.…”

Section: Pair Contact Process With Diffusionmentioning

confidence: 99%

Nonequilibrium phase transitions into absorbing states

Park

2008

Eur. Phys. J. B

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Abstract. Systems with absorbing (trapped) states may exhibit a nonequilibrium phase transition from a noise-free inactive phase into an ever-lasting active phase. We briefly review the absorbing critical phenomena and universality classes, and discuss over the controversial issues on the pair contact process with diffusion (PCPD). Two different approaches are proposed to clarify its universality issue, which unveil strong evidences that the PCPD belongs to a new universality class other than the directed percolation class.

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The non-equilibrium phase transition of the pair-contact process with diffusion

Cited by 87 publications

References 96 publications

Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Pair contact process with diffusion: Failure of master equation field theory

Nonequilibrium phase transitions into absorbing states

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