Mean-field (<i>n</i>,<i>m</i>)-cluster approximation for lattice models

ben‐Avraham, Daniel; Köhler, Jutta

doi:10.1103/physreva.45.8358

Cited by 104 publications

(114 citation statements)

References 23 publications

Supporting

Mentioning

112

Contrasting

Order By: Relevance

“…In a homogeneous pair approximation, the probability of a microscopic configuration is factorized as [41] Q(σ i σ j σ l ) ≈ Q(σ i σ j )Q(σ j σ l ) Q(σ j ) .…”

Section: Appendix B: Homogeneous Pair Approximationmentioning

confidence: 99%

Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks

2013

View full text Add to dashboard Cite

We investigate the effects of local population structure in reaction-diffusion processes representing a contact process (CP) on metapopulations represented as complex networks. Considering a model in which the nodes of a large scale network represent local populations defined in terms of a homogeneous graph, we show by means of extensive numerical simulations that the critical properties of the reaction-diffusion system are independent of the local population structure, even when this one is given by a ordered linear chain. This independence is confirmed by the perfect matching between numerical critical exponents and the results from a heterogeneous mean-field theory suited, in principle, to describe situations of local homogeneous mixing. The analysis of several variations of the reaction-diffusion process allows us to conclude the independence from population structure of the critical properties of CP-like models on metapopulations, and thus of the universality of the reaction-diffusion description of this kind of models.

show abstract

“…In a homogeneous pair approximation, the probability of a microscopic configuration is factorized as [41] Q(σ i σ j σ l ) ≈ Q(σ i σ j )Q(σ j σ l ) Q(σ j ) .…”

Section: Appendix B: Homogeneous Pair Approximationmentioning

confidence: 99%

Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks

2013

View full text Add to dashboard Cite

show abstract

“…One can easily verify that the characteristic time τ scales with DP mean field exponent, τ ∼ (λ − λ c ) −1 , while the density of active sites decays with time at criticality as φ c ∼ t −1 . For the case of the CP, it has been shown that a homogeneous pair approximation (HPA) [38], considering the hierarchy of equations up to second order, yields better estimates of the critical point even in the realistic case of heterogeneous networks [20,39]. We can also follow this HPA approach for the TCP.…”

Section: Mean-field Analysis a Homogeneous Mean-field Theorymentioning

confidence: 99%

Phase transitions with infinitely many absorbing states in complex networks

2013

View full text Add to dashboard Cite

We instigate the properties of the threshold contact process (TCP), a process showing an absorbing-state phase transition with infinitely many absorbing states, on random complex networks. The finite size scaling exponents characterizing the transition are obtained in a heterogeneous mean field (HMF) approximation and compared with extensive simulations, particularly in the case of heterogeneous scale-free networks. We observe that the TCP exhibits the same critical properties as the contact process (CP), which undergoes an absorbing-state phase transition to a single absorbing state. The accordance among the critical exponents of different models and networks leads to conjecture that the critical behavior of the contact process in a HMF theory is a universal feature of absorbing state phase transitions in complex networks, depending only on the locality of the interactions and independent of the number of absorbing states. The conditions for the applicability of the conjecture are discussed considering a parallel with the susceptible-infected-susceptible epidemic spreading model, which in fact belongs to a different universality class in complex networks.

show abstract

“…We now illustrate the standard methods [1,60] how to find the equations of motions for ρ(t) and u(t) in the pair approximation. Introduce the shorthand v = P •• = ρ − u and w = P •• = 1 − 2ρ + u.…”

Section: The Pair Approximation: Two Transitions ?mentioning

confidence: 99%

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

Henkel

Hinrichsen

2004

J. Phys. A: Math. Gen.

107

View full text Add to dashboard Cite

Abstract. The pair-contact process 2A → 3A, 2A → ∅ with diffusion of individual particles is a simple branching-annihilation processes which exhibits a phase transition from an active into an absorbing phase with an unusual type of critical behaviour which had not been seen before. Although the model has attracted considerable interest during the past few years it is not yet clear how its critical behaviour can be characterized and to what extent the diffusive pair-contact process represents an independent universality class. Recent research is reviewed and some standing open questions are outlined.

show abstract

Mean-field (n,m)-cluster approximation for lattice models

Cited by 104 publications

References 23 publications

Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks

Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks

Phase transitions with infinitely many absorbing states in complex networks

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

Contact Info

Product

Resources

About