2006/10/31 by Omar Al Hammal, Juan A. Bonachela, Miguel A. Muñoz +1
Mathematics · Physics and Astronomy · #Class (philosophy) #Computer science #Critical dimension #Critical exponent #Critical point (mathematics) #Fixed point #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical physics #Mathematics #Phase transition #Physics #Pure mathematics #Quantum mechanics #Renormalization group #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Theoretical physics #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2006/12/p12007
published as J. Stat. Mech. (2006) P12007 · 6 pages. 3 Figures. Final version as published in J.Stat.Mech
openalex publication_date 2006/12/07 · arxiv created 2006/12/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 together with creation processes of the form with n ≥2. This class includes the (exactly solvable in one dimension) reversible model 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.