Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0511065 · Physical Review Letters

Nonequilibrium Phase Transition on a Randomly Diluted Lattice

Thomas Vojta, Man Young Lee

Published Jan 27, 2006• 49 citations
arXivHTMLPDF

Abstract

We show that the interplay between geometric criticality and dynamical fluctuations leads to a novel universality class of the contact process on a randomly diluted lattice. The nonequilibrium phase transition across the percolation threshold of the lattice is characterized by unconventional activated (exponential) dynamical scaling and strong Griffiths effects. We calculate the critical behavior in two and three space dimensions, and we also relate our results to the recently found infinite-randomness fixed point in the disordered one-dimensional contact process.

DOI
10.1103/physrevlett.96.035701

Related papers

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

Thomas Vojta, Adam Farquhar, Jason Mast

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 8000x8000 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.

arXiv:0810.1569•Physical Review E•Jan 12, 2009•122 citations

Critical behavior and Griffiths effects in the disordered contact process

Thomas Vojta, Mark E. Dickison

We study the nonequilibrium phase transition in the one-dimensional contact process with quenched spatial disorder by means of large-scale Monte Carlo simulations for times up to 10(9) and system sizes up to 10(7) sites. In agreement with recent predictions of an infinite-randomness fixed point, our simulations demonstrate activated (exponential) dynamical scaling at the critical point. The critical behavior turns out to be universal, even for weak disorder. However, the approach to this asymptotic behavior is extremely slow, with crossover times of the order of 10(4) or larger. In the Griffiths region between the clean and the dirty critical points, we find power-law dynamical behavior 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.

arXiv:cond-mat/0505354•Physical Review E•Sep 27, 2005•110 citations

Monte Carlo simulations of the clean and disordered contact process in three dimensions

Thomas Vojta

The absorbing-state transition in the three-dimensional contact process with and without quenched randomness is investigated by means of Monte Carlo simulations. In the clean case, a reweighting technique is combined with a careful extrapolation of the data to infinite time to determine with high accuracy the critical behavior in the three-dimensional directed percolation universality class. In the presence of quenched spatial disorder, our data demonstrate that the absorbing-state transition is governed by an unconventional infinite-randomness critical point featuring activated dynamical scaling. The critical behavior of this transition does not depend on the disorder strength, i.e., it is universal. Close to the disordered critical point, the dynamics is characterized by the nonuniversal power laws typical of a Griffiths phase. We compare our findings to the results of other numerical methods, and we relate them to a general classification of phase transitions in disordered systems based on the rare region dimensionality.

arXiv:1209.1400•Physical Review E•Nov 30, 2012•35 citations

Multicritical behaviour of the diluted contact process

Sílvio R. Dahmen, Lionel Sittler, Haye Hinrichsen B

We study a contact process on a two-dimensional square lattice which is diluted by randomly removing bonds with probability p . For p <1/2 and varying birth rate λ the model was shown to exhibit a continuous phase transition which belongs to the universality class of strongly disordered directed percolation. The phase transition line terminates in a multicritical point at p = 1/2 and λ = λ * = 3.55(1), where the model can be interpreted as a critical directed percolation process running on a critical isotropic percolation cluster. In the present work we study the multicritical point and its neighbourhood by numerical simulations, discussing possible scaling forms which could describe the critical behaviour at the transition.

arXiv:cond-mat/0610505•Journal of Statistical Mechanics Theory and Experiment•Jan 9, 2007•14 citations

Rare regions and Griffiths singularities at a clean critical point: The five-dimensional disordered contact process

Thomas Vojta, John Igo, José A. Hoyos

We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent z' saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion, which implies that weak disorder is renormalization-group irrelevant, and the rare-region classification, which predicts unconventional behavior. We confirm and illustrate our theory by large-scale Monte Carlo simulations of systems with up to 70(5) sites. We also relate our results to a recently established general relation between the Harris criterion and Griffiths singularities [Phys. Rev. Lett. 112, 075702 (2014)], and we discuss implications for other phase transitions.

arXiv:1405.4337•Physical Review E•Jul 29, 2014•12 citations

QUANTUM PHASE TRANSITIONS ON PERCOLATING LATTICES

Thomas Vojta, José A. Hoyos

When a quantum many-particle system exists on a randomly diluted lattice, its intrinsic thermal and quantum fluctuations coexist with geometric fluctuations due to percolation. In this paper, we explore how the interplay of these fluctuations influences the phase transition at the percolation threshold. While it is well known that thermal fluctuations generically destroy long-range order on the critical percolation cluster, the effects of quantum fluctuations are more subtle. In diluted quantum magnets with and without dissipation, this leads to novel universality classes for the zero-temperature percolation quantum phase transition. Observables involving dynamical correlations display nonclassical scaling behavior that can nonetheless be determined exactly in two dimensions.

arXiv:0707.0658•Recent Progress in Many-Body Theories•Jun 1, 2008•4 citations
We show that the interplay between geometric criticality and dynamical fluctuations leads to a novel universality class of the contact process on a randomly diluted lattice. The nonequilibrium phase transition across the percolation threshold of the lattice is characterized by unconventional activated (exponential) dynamical scaling and strong Griffiths effects. We calculate the critical behavior in two and three space dimensions, and we also relate our results to the recently found infinite-randomness fixed point in the disordered one-dimensional contact process.
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 8000x8000 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.
We study the nonequilibrium phase transition in the one-dimensional contact process with quenched spatial disorder by means of large-scale Monte Carlo simulations for times up to 10(9) and system sizes up to 10(7) sites. In agreement with recent predictions of an infinite-randomness fixed point, our simulations demonstrate activated (exponential) dynamical scaling at the critical point. The critical behavior turns out to be universal, even for weak disorder. However, the approach to this asymptotic behavior is extremely slow, with crossover times of the order of 10(4) or larger. In the Griffiths region between the clean and the dirty critical points, we find power-law dynamical behavior 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.
The absorbing-state transition in the three-dimensional contact process with and without quenched randomness is investigated by means of Monte Carlo simulations. In the clean case, a reweighting technique is combined with a careful extrapolation of the data to infinite time to determine with high accuracy the critical behavior in the three-dimensional directed percolation universality class. In the presence of quenched spatial disorder, our data demonstrate that the absorbing-state transition is governed by an unconventional infinite-randomness critical point featuring activated dynamical scaling. The critical behavior of this transition does not depend on the disorder strength, i.e., it is universal. Close to the disordered critical point, the dynamics is characterized by the nonuniversal power laws typical of a Griffiths phase. We compare our findings to the results of other numerical methods, and we relate them to a general classification of phase transitions in disordered systems based on the rare region dimensionality.
We study a contact process on a two-dimensional square lattice which is diluted by randomly removing bonds with probability p . For p <1/2 and varying birth rate λ the model was shown to exhibit a continuous phase transition which belongs to the universality class of strongly disordered directed percolation. The phase transition line terminates in a multicritical point at p = 1/2 and λ = λ * = 3.55(1), where the model can be interpreted as a critical directed percolation process running on a critical isotropic percolation cluster. In the present work we study the multicritical point and its neighbourhood by numerical simulations, discussing possible scaling forms which could describe the critical behaviour at the transition.
We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent z' saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion, which implies that weak disorder is renormalization-group irrelevant, and the rare-region classification, which predicts unconventional behavior. We confirm and illustrate our theory by large-scale Monte Carlo simulations of systems with up to 70(5) sites. We also relate our results to a recently established general relation between the Harris criterion and Griffiths singularities [Phys. Rev. Lett. 112, 075702 (2014)], and we discuss implications for other phase transitions.
When a quantum many-particle system exists on a randomly diluted lattice, its intrinsic thermal and quantum fluctuations coexist with geometric fluctuations due to percolation. In this paper, we explore how the interplay of these fluctuations influences the phase transition at the percolation threshold. While it is well known that thermal fluctuations generically destroy long-range order on the critical percolation cluster, the effects of quantum fluctuations are more subtle. In diluted quantum magnets with and without dissipation, this leads to novel universality classes for the zero-temperature percolation quantum phase transition. Observables involving dynamical correlations display nonclassical scaling behavior that can nonetheless be determined exactly in two dimensions.