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
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Absorbing state phase transitions with a non-accessible vacuum. / Al Hammal, Omar; Bonachela, Juan A.; Muñoz, Miguel A.
In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2006, No. 12, P12007, 07.12.2006.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 -