Finite-size scaling of directed percolation above the upper critical dimension

Lübeck, S.; Janssen, Hans-Karl

doi:10.1103/physreve.72.016119

Cited by 15 publications

(15 citation statements)

References 32 publications

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“…The same applies to lower moment ratios, which can be determined with higher accuracy, such as ρ 2 C / ρ 2 C . It is now also clear why the slightly more complicated moment ratio proposed in [12] …”

Section: Discussionmentioning

confidence: 99%

Equivalence of conditional and external field ensembles in absorbing-state phase transitions

Pruessner

2007

Phys. Rev. E

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I comment on the relation between two sampling methods for absorbing state models. It is shown that a certain ensemble without external field conditional to activity coincides with the unconditional ensemble for sufficiently small external field. The actual physical processes involved are identical and the derivation of the identity of the scaling behaviour relies on a single (established) scaling law. While the conditional ensemble by construction does not contain information about the system with large external field, it contains all information about the limit of vanishing external field and about the vicinity of the critical point: Finite size scaling as well as critical scaling in the temperature-like variable or in (small) external field.

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Section: Discussionmentioning

confidence: 99%

Equivalence of conditional and external field ensembles in absorbing-state phase transitions

Pruessner

2007

Phys. Rev. E

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“…Unfortunately, the Binder cumulant diverges at the critical point of absorbing phase transitions [41,43]. This behavior is caused by the vanishing steady state fluctuations in the absorbing phase and reflects the different nature of the zeroorder parameter phase in equilibrium and in absorbing phase transitions.…”

Section: Second-order Phase Transition: Tricritical Behaviormentioning

confidence: 99%

“…This behavior is caused by the vanishing steady state fluctuations in the absorbing phase and reflects the different nature of the zeroorder parameter phase in equilibrium and in absorbing phase transitions. A ratio that remains finite at criticality is given by [43] …”

Section: Second-order Phase Transition: Tricritical Behaviormentioning

confidence: 99%

Tricritical Directed Percolation

Lübeck

2006

J Stat Phys

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We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The incorporated higher-order reaction terms lead to a non-trivial phase diagram. In particular, a line of continuous phase transitions is separated by a tricritical point from a line of discontinuous phase transitions. The corresponding tricritical scaling behavior is analyzed in detail, i.e., we determine the critical exponents, various universal scaling functions as well as universal amplitude combinations.

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“…Universal and size-independent moment ratios were studied for absorbing phase transitions in lattice models [29][30][31]. The size independence of moment ratios in lattice systems results from the scaling invariance close to the critical point (see, e.g., Ref.…”

Section: A Determination Of the Critical Pointmentioning

confidence: 99%

Quasistationary simulations of the contact process on quenched networks

et al. 2011

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We present high-accuracy quasistationary (QS) simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs. The critical behavior is analyzed in the framework of the anomalous finite-size scaling which was recently shown to hold for the contact process on annealed networks. It turns out that the quenched topology does not qualitatively change the critical behavior, leading only (as expected) to a shift of the transition point. The anomalous finite-size scaling holds with exactly the same exponents of the annealed case, so we can conclude that heterogeneous mean-field theory works for the contact process on quenched networks, at odds with previous claims. Interestingly, topological correlations induced by the presence of the natural cutoff do not alter the picture.

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Finite-size scaling of directed percolation above the upper critical dimension

Cited by 15 publications

References 32 publications

Equivalence of conditional and external field ensembles in absorbing-state phase transitions

Equivalence of conditional and external field ensembles in absorbing-state phase transitions

Tricritical Directed Percolation

Quasistationary simulations of the contact process on quenched networks

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