Abstract
The directed bond percolation process is an important model in statistical physics. 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 higher orders of perturbation theory and is focused on the most complicated Feynman diagrams with problems in calculation. The anomalous dimensions are computed up to three-loop order in ε = 4 − d.
Highlights
The directed bond percolation process (DP) constitutes one of the simplest non-equilibrium systems in statistical physics [1,2,3]
The DP universal class is important for the non-equilibrium physics and it may be considered as important as the Ising model for the static equilibrium systems
An important method for an analysis of the second order phase transition is the renormalization group (RG) approach [4] and the ε-expansion where ε is the deviation from the upper critical dimension dc = 4
Summary
The directed bond percolation process (DP) constitutes one of the simplest non-equilibrium systems in statistical physics [1,2,3]. It is one of the basic examples of an absorbing phase transition between an absorbing and active state. By means of the scheme the renormalized Green function is obtained by R operation [4, 5] on Green function Within this procedure anomalous dimensions γ are expressed in terms of irreducible renormalized Feynman diagrams, and the calculation of renormalization constants can be entirely skipped [6, 7]. The universal quantities are calculable in the form of the ε-expansion and they are independent of the choice of the renormalization scheme [4]
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