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

Journal of Statistical Mechanics Theory and Experiment

Critical behavior of the absorbing transition of branching and annihilating bosonic random walkers

C. Argolo, Pedro H. Barros, Iram Gléria, Fabiana Carvalho dos Anjos, M. L. Lyra

Published Aug 12, 2015• 2 citations
Publisher

Abstract

In this work, we investigate the critical behavior of a model describing the parity-conserving branching and annihilating process of random walkers. The model is simulated on a one dimensional lattice on which the sites can be occupied by multiple particles with a finite annhilation probability. We determine the threshold of the phase transition between the statistically stationary active state and the absorbing state. From steady-state simulations and a finite-size scaling analysis, we calculate the order-parameter, order-parameter fluctuations, and spacial correlation length critical exponents. Further, we follow the short-time critical relaxation to provide a set of relevant dynamical critical exponents. We check the validity of the hyperscaling relation for both sets of stationary and dynamical critical exponents. These are consistent with the BARW-PC universality class.

DOI
10.1088/1742-5468/2015/08/p08006

Related papers

Critical behavior in a model of random walkers in processes with conservation of parity, branching, multiple occupation and annihilation.

Fabiana Carvalho dos Anjos

In this dissertation we address the problem of second order phase transitions with absorbing states. We analyze the critical behavior of a one dimensional model simulated on one dimensional chains. The sites on the linear chain can be multiple occupied by particles that annhilates each other with a finite probability. It also presents parity-conserving branching with an even number of offsprings. The number of particles are constant modulo 2. We determine the threshold of the phase transition between the statistically stationary active state and the absorbing state. From steady-state simulations and a finite-size scaling analysis, we calculate the order-parameter, order-parameter fluctuations, and special correlation length critical exponents. We also followed the short-time critical relaxation to determine some dynamical critical exponents. The hyperscaling relation is checked for both sets of stationary and dynamical critical exponents which we found to be consistent with the BARW-PC universality class.

•Jul 27, 2016•0 citations

Critical behavior of branching annihilating random walks with an odd number of offsprings

Iwan Jensen

Recently, Takayasu and Tretyakov [Phys. Rev. Lett. 68, 3060 (1992)] studied branching annihilating random walks with n=1-5 offsprings. These models exhibit a continuous phase transition to an absorbing state. Steady-state simulations yielded an estimate for the order parameter critical exponent \ensuremath{\beta} different from that of directed percolation. This result is quite surprising, as the universality class of directed percolation is known to be very robust. I have studied the critical behavior of the one-dimensional model with n=1 and 3 using time-dependent Monte Carlo simulations, and determined three critical exponents, all of which are in agreement with directed percolation.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jan 1, 1993•66 citations

Critical exponents for branching annihilating random walks with an even number of offspring

Iwan Jensen

Recently, Takayasu and Tretyakov [Phys. Rev. Lett. 68, 3060 (1992)] studied branching annihilating random walks (BAWs) with n=1--5 offspring. These models exhibit a continuous phase transition to an absorbing state. For odd n the models belong to the universality class of directed percolation. For even n the particle number is conserved modulo 2 and the critical behavior is not compatible with directed percolation. In this article I study the BAW with n=4 using time-dependent simulations and finite-size scaling, obtaining precise estimates for various critical exponents. The results are consistent with the conjecture: \ensuremath{\beta}/${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$=1/2, ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\parallel}}}$/${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$=7/4, \ensuremath{\gamma}=0, \ensuremath{\delta}=2/7, \ensuremath{\eta}=0, and ${\mathrm{\ensuremath{\delta}}}_{\mathit{h}}$=9/2. These critical exponents characterize, respectively, the dependence of the order parameter (\ensuremath{\beta}/${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$) and relaxation time (${\ensuremath{\nu}}_{\mathrm{\ensuremath{\parallel}}}$/${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$) on system size, the growth of fluctuations (\ensuremath{\gamma}) close to the critical point, the long-time behavior of the probability of survival (\ensuremath{\delta}) and average number of particles (\ensuremath{\eta}) when starting at time zero with just two particles, and finally the decay of the order parameter (${\mathrm{\ensuremath{\delta}}}_{\mathit{h}}$) at the critical point in the presence of an external source.

arXiv:cond-mat/9405006•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Nov 1, 1994•140 citations

Continuously varying critical order-parameter fluctuations in a parity conserving absorbing-state transition with long-range diffusion

T. Laise, Pedro H. Barros, C. Argolo +1 more

Abstract We study the critical order parameter fluctuations of the absorbing-state phase-transition exhibited by branching and annihilating random walkers performing anomalous diffusion in a linear chain. The diffusion process is considered to follow a power-law distribution of jump lengths with a typical decay exponent α . We focus in the case of parity conserving dynamics for which deviations from the usual directed percolation universality class have been previously demonstrated even for the limiting cases of normal diffusion. Anomalous diffusion induces a continuous change of the critical exponents. By performing a finite-size scaling analysis of simulation data, we show that the critical order parameter moment ratio also varies continuously with α . We unveil that the critical order parameter distribution evolves from a nearly Gaussian to an exponential form as the range of the jump distribution is increased up to the limit α = 5 / 2 on which the active state predominates for any finite branching probability.

Journal of Statistical Mechanics Theory and Experiment•Nov 1, 2016•2 citations

DIRECTED PERCOLATION AND OTHER SYSTEMS WITH ABSORBING STATES: IMPACT OF BOUNDARIES

PER FRÖJDH, MARTIN HOWARD, K. B. Lauritsen

We review the critical behavior of nonequilibrium systems, such as directed percolation (DP) and branching-annihilating random walks (BARW), which possess phase transitions into absorbing states. After reviewing the bulk scaling behavior of these models, we devote the main part of this review to analyzing the impact of walls on their critical behavior. We discuss the possible boundary universality classes for the DP and BARW models, which can be described by a general scaling theory which allows for two independent surface exponents in addition to the bulk critical exponents. Above the upper critical dimension d c , we review the use of mean field theories, whereas in the regime d<d c , where fluctuations are important, we examine the application of field theoretic methods. Of particular interest is the situation in d=1, which has been extensively investigated using numerical simulations and series expansions. Although DP and BARW fit into the same scaling theory, they can still show very different surface behavior: for DP some exponents are degenerate, a property not shared with the BARW model. Moreover, a "hidden" duality symmetry of BARW in d=1 is broken by the boundary and this relates exponents and boundary conditions in an intricate way.

arXiv:cond-mat/0101387•International Journal of Modern Physics B•May 20, 2001•33 citations

Branching annihilating random walks with parity conservation on a square lattice

György Szabó, Maria Augusta Santos

Using Monte Carlo simulations we have studied the transition from an ``active'' steady state to an absorbing ``inactive'' state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the first model the randomly walking particles annihilate when they meet and the branching process creates two additional particles; in the second case we distinguish particles and antiparticles created and annihilated in pairs. Quite distinct critical behavior is found in the two cases, raising the question of what determines universality in these kinds of systems.

arXiv:cond-mat/9812005•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Mar 1, 1999•8 citations
In this work, we investigate the critical behavior of a model describing the parity-conserving branching and annihilating process of random walkers. The model is simulated on a one dimensional lattice on which the sites can be occupied by multiple particles with a finite annhilation probability. We determine the threshold of the phase transition between the statistically stationary active state and the absorbing state. From steady-state simulations and a finite-size scaling analysis, we calculate the order-parameter, order-parameter fluctuations, and spacial correlation length critical exponents. Further, we follow the short-time critical relaxation to provide a set of relevant dynamical critical exponents. We check the validity of the hyperscaling relation for both sets of stationary and dynamical critical exponents. These are consistent with the BARW-PC universality class.
In this dissertation we address the problem of second order phase transitions with absorbing states. We analyze the critical behavior of a one dimensional model simulated on one dimensional chains. The sites on the linear chain can be multiple occupied by particles that annhilates each other with a finite probability. It also presents parity-conserving branching with an even number of offsprings. The number of particles are constant modulo 2. We determine the threshold of the phase transition between the statistically stationary active state and the absorbing state. From steady-state simulations and a finite-size scaling analysis, we calculate the order-parameter, order-parameter fluctuations, and special correlation length critical exponents. We also followed the short-time critical relaxation to determine some dynamical critical exponents. The hyperscaling relation is checked for both sets of stationary and dynamical critical exponents which we found to be consistent with the BARW-PC universality class.
Recently, Takayasu and Tretyakov [Phys. Rev. Lett. 68, 3060 (1992)] studied branching annihilating random walks with n=1-5 offsprings. These models exhibit a continuous phase transition to an absorbing state. Steady-state simulations yielded an estimate for the order parameter critical exponent \ensuremath{\beta} different from that of directed percolation. This result is quite surprising, as the universality class of directed percolation is known to be very robust. I have studied the critical behavior of the one-dimensional model with n=1 and 3 using time-dependent Monte Carlo simulations, and determined three critical exponents, all of which are in agreement with directed percolation.
Recently, Takayasu and Tretyakov [Phys. Rev. Lett. 68, 3060 (1992)] studied branching annihilating random walks (BAWs) with n=1--5 offspring. These models exhibit a continuous phase transition to an absorbing state. For odd n the models belong to the universality class of directed percolation. For even n the particle number is conserved modulo 2 and the critical behavior is not compatible with directed percolation. In this article I study the BAW with n=4 using time-dependent simulations and finite-size scaling, obtaining precise estimates for various critical exponents. The results are consistent with the conjecture: \ensuremath{\beta}/${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$=1/2, ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\parallel}}}$/${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$=7/4, \ensuremath{\gamma}=0, \ensuremath{\delta}=2/7, \ensuremath{\eta}=0, and ${\mathrm{\ensuremath{\delta}}}_{\mathit{h}}$=9/2. These critical exponents characterize, respectively, the dependence of the order parameter (\ensuremath{\beta}/${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$) and relaxation time (${\ensuremath{\nu}}_{\mathrm{\ensuremath{\parallel}}}$/${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$) on system size, the growth of fluctuations (\ensuremath{\gamma}) close to the critical point, the long-time behavior of the probability of survival (\ensuremath{\delta}) and average number of particles (\ensuremath{\eta}) when starting at time zero with just two particles, and finally the decay of the order parameter (${\mathrm{\ensuremath{\delta}}}_{\mathit{h}}$) at the critical point in the presence of an external source.
Abstract We study the critical order parameter fluctuations of the absorbing-state phase-transition exhibited by branching and annihilating random walkers performing anomalous diffusion in a linear chain. The diffusion process is considered to follow a power-law distribution of jump lengths with a typical decay exponent α . We focus in the case of parity conserving dynamics for which deviations from the usual directed percolation universality class have been previously demonstrated even for the limiting cases of normal diffusion. Anomalous diffusion induces a continuous change of the critical exponents. By performing a finite-size scaling analysis of simulation data, we show that the critical order parameter moment ratio also varies continuously with α . We unveil that the critical order parameter distribution evolves from a nearly Gaussian to an exponential form as the range of the jump distribution is increased up to the limit α = 5 / 2 on which the active state predominates for any finite branching probability.
We review the critical behavior of nonequilibrium systems, such as directed percolation (DP) and branching-annihilating random walks (BARW), which possess phase transitions into absorbing states. After reviewing the bulk scaling behavior of these models, we devote the main part of this review to analyzing the impact of walls on their critical behavior. We discuss the possible boundary universality classes for the DP and BARW models, which can be described by a general scaling theory which allows for two independent surface exponents in addition to the bulk critical exponents. Above the upper critical dimension d c , we review the use of mean field theories, whereas in the regime d<d c , where fluctuations are important, we examine the application of field theoretic methods. Of particular interest is the situation in d=1, which has been extensively investigated using numerical simulations and series expansions. Although DP and BARW fit into the same scaling theory, they can still show very different surface behavior: for DP some exponents are degenerate, a property not shared with the BARW model. Moreover, a "hidden" duality symmetry of BARW in d=1 is broken by the boundary and this relates exponents and boundary conditions in an intricate way.
Using Monte Carlo simulations we have studied the transition from an ``active'' steady state to an absorbing ``inactive'' state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the first model the randomly walking particles annihilate when they meet and the branching process creates two additional particles; in the second case we distinguish particles and antiparticles created and annihilated in pairs. Quite distinct critical behavior is found in the two cases, raising the question of what determines universality in these kinds of systems.