Numerical Calculation of Scaling Exponents of Percolation Process in the Framework of Renormalization Group Approach
1 Department of Theoretical Physics, St. Petersburg State University, Uljanovskaja 1, 198504 St. Petersburg-Petrodvorets, Russia
2 Department of Theoretical Physics, SAS, Institute of Experimental Physics, Watsonova 47, 040 01 Košice, Slovakia
3 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Joliot-Curie 6, 141980 Dubna, Moscow Region, Russia
4 Faculty of Science, P. J. Šafárik University, Šrobárova 2, 041 54 Košice, Slovakia
5 Fakultät für Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany
Published online: 9 February 2016
The renormalization group theory is used to the study of the directed bond percolation (Gribov process) near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group functions in the ε-expansion where ε is the deviation from the upper critical dimension dc = 4. Within this procedure anomalous dimensions γ are expressed in terms of irreducible renormalized Feynman diagrams and thus the calculation of renormalization constants could be entirely skipped. The renormalization group is included by means of the R operation, and for computational purposes we choose the null momentum subtraction scheme.
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