TY - CONF

T1 - Anomalous dimensions of directed bond percolation process

T2 - 10th International Conference on Chaotic Modeling and Simulation, CHAOS 2017

AU - Adzhemyan, L. Ts

AU - Hnatic, M.

AU - Kompaniets, M. V.

AU - Lucivjanský, T.

AU - Mižišin, L.

N1 - Funding Information: The work was supported by VEGA grant No. 1/0345/17 of the Ministry of Education, Science, Research and Sport of the Slovak Republic. The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008). L. M. would like to thank Martin Vaľa for his help with the numerical analysis in the JINR Dubna. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2017

Y1 - 2017

N2 - Directed bond percolation process is an important model in statistical physics. It provides a paramount example of non-equilibrium phase transitions. By now its universal properties are known only up to the second-order of the perturbation theory. Here, our aim is to put forward a numerical technique with anomalous dimensions of directed percolation to the higher orders of perturbation theory. It is based on the perturbative renormalization scheme in deviation from the upper critical dimension, ϵ = 4-d. Universal quantities are expressed in terms of irreducible renormalized Feynman diagrams and there is no need for calculation of renormalization constants. A numerical evaluation of integrals has been performed using the Vegas algorithm from the Cuba library. Whitin the framework, the anomalous dimensions are computed up to three-loop order in ϵ.

AB - Directed bond percolation process is an important model in statistical physics. It provides a paramount example of non-equilibrium phase transitions. By now its universal properties are known only up to the second-order of the perturbation theory. Here, our aim is to put forward a numerical technique with anomalous dimensions of directed percolation to the higher orders of perturbation theory. It is based on the perturbative renormalization scheme in deviation from the upper critical dimension, ϵ = 4-d. Universal quantities are expressed in terms of irreducible renormalized Feynman diagrams and there is no need for calculation of renormalization constants. A numerical evaluation of integrals has been performed using the Vegas algorithm from the Cuba library. Whitin the framework, the anomalous dimensions are computed up to three-loop order in ϵ.

KW - Directed bond percolation

KW - Multi-dimensional integration

KW - Non-equilibrium phase transition

KW - The renormalization group

UR - http://www.scopus.com/inward/record.url?scp=85072575062&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:85072575062

SP - 41

EP - 58

Y2 - 30 May 2017 through 2 June 2017

ER -