### Abstract

We analyse from the renormalization group perspective a universality class of reaction.diffusion systems with absorbing states. In this class, models where the vacuum state is not accessible are represented as the set of reactions 2A → A together with creation processes of the form A → nA with n ≥ 2. This class includes the (exactly solvable in one dimension) reversible model 2A ↔ A as a particular example, as well as many other non-reversible sets of reactions, proving that reversibility is not the main feature of this class as previously thought. By using field theoretical techniques we show that the critical point appears at zero creation rate (in accordance with known results for the reversible case) and it is controlled by the well known pair-coagulation renormalization group fixed point, with non-trivial exactly computable critical exponents in any dimension. Finally, we report on Monte Carlo simulations, confirming the field theoretical predictions in one and two dimensions for various reversible and non-reversible sets of reactions.

Language | English |
---|---|

Article number | P12007 |

Number of pages | 14 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2006 |

Issue number | 12 |

DOIs | |

Publication status | Published - 7 Dec 2006 |

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### Keywords

- phase transitions into absorbing states
- vacuum
- Monte Carlo simulations

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2006*(12), [P12007]. https://doi.org/10.1088/1742-5468/2006/12/P12007

}

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2006, no. 12, P12007. https://doi.org/10.1088/1742-5468/2006/12/P12007

**Absorbing state phase transitions with a non-accessible vacuum.** / Al Hammal, Omar; Bonachela, Juan A.; Muñoz, Miguel A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Absorbing state phase transitions with a non-accessible vacuum

AU - Al Hammal, Omar

AU - Bonachela, Juan A.

AU - Muñoz, Miguel A.

PY - 2006/12/7

Y1 - 2006/12/7

N2 - We analyse from the renormalization group perspective a universality class of reaction.diffusion systems with absorbing states. In this class, models where the vacuum state is not accessible are represented as the set of reactions 2A → A together with creation processes of the form A → nA with n ≥ 2. This class includes the (exactly solvable in one dimension) reversible model 2A ↔ A as a particular example, as well as many other non-reversible sets of reactions, proving that reversibility is not the main feature of this class as previously thought. By using field theoretical techniques we show that the critical point appears at zero creation rate (in accordance with known results for the reversible case) and it is controlled by the well known pair-coagulation renormalization group fixed point, with non-trivial exactly computable critical exponents in any dimension. Finally, we report on Monte Carlo simulations, confirming the field theoretical predictions in one and two dimensions for various reversible and non-reversible sets of reactions.

AB - We analyse from the renormalization group perspective a universality class of reaction.diffusion systems with absorbing states. In this class, models where the vacuum state is not accessible are represented as the set of reactions 2A → A together with creation processes of the form A → nA with n ≥ 2. This class includes the (exactly solvable in one dimension) reversible model 2A ↔ A as a particular example, as well as many other non-reversible sets of reactions, proving that reversibility is not the main feature of this class as previously thought. By using field theoretical techniques we show that the critical point appears at zero creation rate (in accordance with known results for the reversible case) and it is controlled by the well known pair-coagulation renormalization group fixed point, with non-trivial exactly computable critical exponents in any dimension. Finally, we report on Monte Carlo simulations, confirming the field theoretical predictions in one and two dimensions for various reversible and non-reversible sets of reactions.

KW - phase transitions into absorbing states

KW - vacuum

KW - Monte Carlo simulations

UR - http://www.scopus.com/inward/record.url?scp=42749107353&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2006/12/P12007

DO - 10.1088/1742-5468/2006/12/P12007

M3 - Article

VL - 2006

JO - Journal of Statistical Mechanics: Theory and Experiment

T2 - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 12

M1 - P12007

ER -