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:0903.4222 · Physical Review E

Crossover from the parity-conserving pair contact process with diffusion to other universality classes

Su‐Chan Park, Hyunggyu Park

Published May 28, 2009• 11 citations
arXivHTMLPDF

Abstract

The pair contact process with diffusion (PCPD) with modulo 2 conservation (PCPD2) [ 2A-->4A , 2A-->0 ] is studied in one dimension, focused on the crossover to other well established universality classes: the directed Ising (DI) and the directed percolation (DP). First, we show that the PCPD2 shares the critical behaviors with the PCPD, both with and without directional bias. Second, the crossover from the PCPD2 to the DI is studied by including a parity-conserving single-particle process (A-->3A) . We find the crossover exponent 1/varphi_{1}=0.57(3) , which is argued to be identical to that of the PCPD-to-DP crossover by adding A-->2A . This suggests that the PCPD universality class has a well-defined fixed point distinct from the DP. Third, we study the crossover from a hybrid-type reaction-diffusion process belonging to the DP [ 3A-->5A , 2A-->0 ] to the DI by adding A-->3A . We find 1/varphi_{2}=0.73(4) for the DP-to-DI crossover. The inequality of varphi_{1} and varphi_{2} further supports the non-DP nature of the PCPD scaling. Finally, we introduce a symmetry-breaking field in the dual spin language to study the crossover from the PCPD2 to the DP. We find 1/varphi_{3}=1.23(10) , which is associated with a new independent route from the PCPD to the DP.

DOI
10.1103/physreve.79.051130

Related papers

Crossover from the pair contact process with diffusion to directed percolation

Su‐Chan Park, Hyunggyu Park

Crossover behaviors from the pair contact process with diffusion (PCPD) and the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one dimension by introducing a single particle annihilation and/or branching dynamics. The crossover exponents phi are estimated numerically as 1/phi approximately 0.58 +/- 0.03 for the PCPD and 1/phi approximately 0.49+/-0.02 for the DPCPD. Nontriviality of the PCPD crossover exponent strongly supports the non-DP nature of the PCPD critical scaling, which is further evidenced by the anomalous critical amplitude scaling near the PCPD point. In addition, we find that the DPCPD crossover is consistent with the mean field prediction of the tricritical DP class as expected.

arXiv:cond-mat/0512076•Physical Review E•Feb 16, 2006•18 citations

Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion

Su‐Chan Park

The one-dimensional pair contact process with diffusion (PCPD), an interacting particle system with diffusion, pair annihilation, and creation by pairs, has defied consensus about the universality class to which it belongs. An argument by Hinrichsen [Physica A 361, 457 (2006)PHYADX0378-437110.1016/j.physa.2005.06.101] claims that freely diffusing particles in the PCPD should play the same role as frozen particles when it comes to the critical behavior. Therefore, the PCPD is claimed to have the same critical phenomena as a model with infinitely many absorbing states that belongs to the directed percolation (DP) universality class. To investigate if diffusing particles are really indistinguishable from frozen particles in the sense of the renormalization group, we study numerically a variation of the PCPD by introducing a nonorder field associated with infinitely many absorbing states. We find that a crossover from the PCPD to DP occurs due to the nonorder field. By studying a similar model, we exclude the possibility that the mere introduction of a nonorder field to one model can entail a nontrivial crossover to another model in the same universality class, thus we attribute the observed crossover to the difference of the universality class of the PCPD from the DP class.

arXiv:1707.03948•Physical review. E•Sep 11, 2017•1 citation

Driven Pair Contact Process with Diffusion

Su‐Chan Park, Hyunggyu Park

The pair contact process with diffusion (PCPD) has been recently investigated extensively, but its critical behavior is not yet clearly established. By introducing biased diffusion, we show that the external driving is relevant and the driven PCPD exhibits a mean-field-type critical behavior even in one dimension. In systems which can be described by a single-species bosonic field theory, the Galilean invariance guarantees that the driving is irrelevant. The well-established directed percolation (DP) and parity-conserving (PC) classes are such examples. This leads us to conclude that the PCPD universality class should be distinct from the DP or the PC class. Moreover, it implies that the PCPD is generically a multispecies model and a field theory of two species is suitable for proper description.

arXiv:cond-mat/0406606•Physical Review Letters•Feb 17, 2005•27 citations

Universality class of absorbing transitions with continuously varying critical exponents

Jae Dong Noh, Hyunggyu Park

The well-established universality classes of absorbing critical phenomena are directed percolation (DP) and directed Ising (DI) classes. Recently, the pair contact process with diffusion (PCPD) has been investigated extensively and claimed to exhibit a different type of critical phenomenon distinct from both DP and DI classes. Noticing that the PCPD possesses a long-term memory effect, we introduce a generalized version of the PCPD (GPCPD) with a parameter controlling the memory strength. The GPCPD connects the DP fixed point to the PCPD point continuously. Monte Carlo simulations strongly suggest that the GPCPD displays, to our knowledge, novel critical phenomena which are characterized by continuously varying critical exponents. The same critical behaviors are also observed in models where two species of particles are coupled cyclically. We present one possible scenario that the long-term memory may serve as a marginal perturbation to the ordinary DP fixed point.

arXiv:cond-mat/0109516•Physical Review E•Jan 30, 2004•53 citations

Universality class of the pair contact process with diffusion

Frank Smallenburg, G. T. Barkema

The pair contact process with diffusion (PCPD) is studied with a standard Monte Carlo approach and with simulations at fixed densities. A standard analysis of the simulation results, based on the particle densities or on the pair densities, yields inconsistent estimates for the critical exponents. However, if a well-chosen linear combination of the particle and pair densities is used, leading corrections can be suppressed, and consistent estimates for the independent critical exponents delta=0.16(2) , beta=0.28(2) , and z=1.58 are obtained. Since these estimates are also consistent with their values in directed percolation (DP), we conclude that the PCPD falls in the same universality class as DP.

arXiv:0710.3692•Physical Review E•Sep 23, 2008•16 citations

Well-defined set of exponents for a pair contact process with diffusion

Kwangho Park, In-mook Kim

Recently it was suggested that a pair contact process with diffusion (PCPD) might represent an independent new universality class different from the directed percolation (DP) and the parity conservation (PC) class. The dynamics in the PCPD are usually controlled by two independent parameters. The critical exponents for the PCPD are known to have different values for varying values of the two independent parameters. However, once the diffusion and annihilation (or coagulation) rate in the PCPD is tuned in a way that the process without offspring production is exactly solvable, a well-defined set of the exponents for the PCPD is obtained. Then dynamics are controlled by only one independent parameter. The obtained critical exponents are different than those of DP and PC. The critical exponents satisfy the generalized hyperscaling relation within numerical errors.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 28, 2002•31 citations
The pair contact process with diffusion (PCPD) with modulo 2 conservation (PCPD2) [ 2A-->4A , 2A-->0 ] is studied in one dimension, focused on the crossover to other well established universality classes: the directed Ising (DI) and the directed percolation (DP). First, we show that the PCPD2 shares the critical behaviors with the PCPD, both with and without directional bias. Second, the crossover from the PCPD2 to the DI is studied by including a parity-conserving single-particle process (A-->3A) . We find the crossover exponent 1/varphi_{1}=0.57(3) , which is argued to be identical to that of the PCPD-to-DP crossover by adding A-->2A . This suggests that the PCPD universality class has a well-defined fixed point distinct from the DP. Third, we study the crossover from a hybrid-type reaction-diffusion process belonging to the DP [ 3A-->5A , 2A-->0 ] to the DI by adding A-->3A . We find 1/varphi_{2}=0.73(4) for the DP-to-DI crossover. The inequality of varphi_{1} and varphi_{2} further supports the non-DP nature of the PCPD scaling. Finally, we introduce a symmetry-breaking field in the dual spin language to study the crossover from the PCPD2 to the DP. We find 1/varphi_{3}=1.23(10) , which is associated with a new independent route from the PCPD to the DP.
Crossover behaviors from the pair contact process with diffusion (PCPD) and the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one dimension by introducing a single particle annihilation and/or branching dynamics. The crossover exponents phi are estimated numerically as 1/phi approximately 0.58 +/- 0.03 for the PCPD and 1/phi approximately 0.49+/-0.02 for the DPCPD. Nontriviality of the PCPD crossover exponent strongly supports the non-DP nature of the PCPD critical scaling, which is further evidenced by the anomalous critical amplitude scaling near the PCPD point. In addition, we find that the DPCPD crossover is consistent with the mean field prediction of the tricritical DP class as expected.
The one-dimensional pair contact process with diffusion (PCPD), an interacting particle system with diffusion, pair annihilation, and creation by pairs, has defied consensus about the universality class to which it belongs. An argument by Hinrichsen [Physica A 361, 457 (2006)PHYADX0378-437110.1016/j.physa.2005.06.101] claims that freely diffusing particles in the PCPD should play the same role as frozen particles when it comes to the critical behavior. Therefore, the PCPD is claimed to have the same critical phenomena as a model with infinitely many absorbing states that belongs to the directed percolation (DP) universality class. To investigate if diffusing particles are really indistinguishable from frozen particles in the sense of the renormalization group, we study numerically a variation of the PCPD by introducing a nonorder field associated with infinitely many absorbing states. We find that a crossover from the PCPD to DP occurs due to the nonorder field. By studying a similar model, we exclude the possibility that the mere introduction of a nonorder field to one model can entail a nontrivial crossover to another model in the same universality class, thus we attribute the observed crossover to the difference of the universality class of the PCPD from the DP class.
The pair contact process with diffusion (PCPD) has been recently investigated extensively, but its critical behavior is not yet clearly established. By introducing biased diffusion, we show that the external driving is relevant and the driven PCPD exhibits a mean-field-type critical behavior even in one dimension. In systems which can be described by a single-species bosonic field theory, the Galilean invariance guarantees that the driving is irrelevant. The well-established directed percolation (DP) and parity-conserving (PC) classes are such examples. This leads us to conclude that the PCPD universality class should be distinct from the DP or the PC class. Moreover, it implies that the PCPD is generically a multispecies model and a field theory of two species is suitable for proper description.
The well-established universality classes of absorbing critical phenomena are directed percolation (DP) and directed Ising (DI) classes. Recently, the pair contact process with diffusion (PCPD) has been investigated extensively and claimed to exhibit a different type of critical phenomenon distinct from both DP and DI classes. Noticing that the PCPD possesses a long-term memory effect, we introduce a generalized version of the PCPD (GPCPD) with a parameter controlling the memory strength. The GPCPD connects the DP fixed point to the PCPD point continuously. Monte Carlo simulations strongly suggest that the GPCPD displays, to our knowledge, novel critical phenomena which are characterized by continuously varying critical exponents. The same critical behaviors are also observed in models where two species of particles are coupled cyclically. We present one possible scenario that the long-term memory may serve as a marginal perturbation to the ordinary DP fixed point.
The pair contact process with diffusion (PCPD) is studied with a standard Monte Carlo approach and with simulations at fixed densities. A standard analysis of the simulation results, based on the particle densities or on the pair densities, yields inconsistent estimates for the critical exponents. However, if a well-chosen linear combination of the particle and pair densities is used, leading corrections can be suppressed, and consistent estimates for the independent critical exponents delta=0.16(2) , beta=0.28(2) , and z=1.58 are obtained. Since these estimates are also consistent with their values in directed percolation (DP), we conclude that the PCPD falls in the same universality class as DP.
Recently it was suggested that a pair contact process with diffusion (PCPD) might represent an independent new universality class different from the directed percolation (DP) and the parity conservation (PC) class. The dynamics in the PCPD are usually controlled by two independent parameters. The critical exponents for the PCPD are known to have different values for varying values of the two independent parameters. However, once the diffusion and annihilation (or coagulation) rate in the PCPD is tuned in a way that the process without offspring production is exactly solvable, a well-defined set of the exponents for the PCPD is obtained. Then dynamics are controlled by only one independent parameter. The obtained critical exponents are different than those of DP and PC. The critical exponents satisfy the generalized hyperscaling relation within numerical errors.