Precise bond percolation thresholds on several four-dimensional lattices
Abstract
We study bond percolation on several four-dimensional (4D) lattices, including the simple (hyper) cubic (SC), the SC with combinations of nearest neighbors and second nearest neighbors (SC-NN+2NN), the body-centered-cubic (bcc), and the face-centered-cubic (fcc) lattices, using an efficient single-cluster growth algorithm. For the SC lattice, we find pc=0.160 131 2 (2 ) , which confirms previous results (based on other methods), and find a new value pc=0.035 827 (1 ) for the SC-NN+2NN lattice, which was not studied previously for bond percolation. For the 4D bcc and fcc lattices, we obtain pc=0.074 212 (1 ) and 0.049 517 (1 ) , which are substantially more precise than previous values. We also find critical exponents τ =2.3135 (5 ) and Ω =0.40 (3 ) , consistent with previous numerical results and the recent four-loop series result of Gracey [Phys. Rev. D 92, 025012 (2015), 10.1103/PhysRevD.92.025012].
- Publication:
-
Physical Review Research
- Pub Date:
- January 2020
- DOI:
- 10.1103/PhysRevResearch.2.013067
- arXiv:
- arXiv:1910.11408
- Bibcode:
- 2020PhRvR...2a3067X
- Keywords:
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- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics
- E-Print:
- Phys. Rev. Research 2, 013067 (2020)