Absorbing state phase transitions with quenched disorder

Hooyberghs, Jef; Iglói, Ferenc; Vanderzande, Carlo

doi:10.1103/physreve.69.066140

Cited by 122 publications

(138 citation statements)

References 52 publications

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“…Its behavior close to the dirty critical point λ c can be obtained within the strong disorder renormalization group method [31,36,38]. When approaching the phase transition, z ′ diverges as…”

Section: Griffiths Singularitiesmentioning

confidence: 97%

Infinite-randomness critical point in the two-dimensional disordered contact process

2009

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We study the nonequilibrium phase transition in the two-dimensional contact process on a randomly diluted lattice by means of large-scale Monte-Carlo simulations for times up to 10 10 and system sizes up to 8000 × 8000 sites. Our data provide strong evidence for the transition being controlled by an exotic infinite-randomness critical point with activated (exponential) dynamical scaling. We calculate the critical exponents of the transition and find them to be universal, i.e., independent of disorder strength. The Griffiths region between the clean and the dirty critical points exhibits power-law dynamical scaling with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder. Our results are of importance beyond absorbing state transitions because according to a strong-disorder renormalization group analysis, our transition belongs to the universality class of the two-dimensional random transverse-field Ising model.

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Section: Griffiths Singularitiesmentioning

confidence: 97%

Infinite-randomness critical point in the two-dimensional disordered contact process

2009

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“…An RG study by (Hooyberghs et al, 2002) showed that in case of strong enough disorder the critical behavior is controlled by an infinite randomness fixed point (IRFP), the static exponents of which in 1d are…”

Section: Quench Disordered Dp Systemsmentioning

confidence: 99%

Universality classes in nonequilibrium lattice systems

2004

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This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.

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“…(16,19), the exponent x ′ has then been calculated from The ratio of exponents η/δ measured in Monte Carlo simulations for different values of β. The value at β = 0 is the SDRG prediction for the one-dimensional random contact process [23].…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

Infinite randomness critical behavior of the contact process on networks with long-range connections

Juhász¹,

Kovács²

2013

J. Stat. Mech.

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Abstract. The contact process and the slightly different susceptible-infectedsusceptible model are studied on long-range connected networks in the presence of random transition rates by means of a strong disorder renormalization group method and Monte Carlo simulations. We focus on the case where the connection probability decays with the distance l as p(l) ≃ βl −2 in one dimension. Here, the graph dimension of the network can be continuously tuned with β. The critical behavior of the models is found to be described by an infinite randomness fixed point which manifests itself in logarithmic dynamical scaling. Estimates of the complete set of the critical exponents, which are found to vary with the graph dimension, are provided by different methods. According to the results, the additional disorder of transition rates does not alter the infinite randomness critical behavior induced by the disordered topology of the underlying random network. This finding opens up the possibility of the application of an alternative tool, the strong disorder renormalization group method to dynamical processes on topologically disordered structures. As the random transverse-field Ising model falls into the same universality class as the random contact process, the results can be directly transferred to that model defined on the same networks.

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Absorbing state phase transitions with quenched disorder

Cited by 122 publications

References 52 publications

Infinite-randomness critical point in the two-dimensional disordered contact process

Infinite-randomness critical point in the two-dimensional disordered contact process

Universality classes in nonequilibrium lattice systems

Infinite randomness critical behavior of the contact process on networks with long-range connections

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