• DOI:10.1103/PhysRevResearch.2.013067
• Corpus ID: 204915841

Precise bond percolation thresholds on several four-dimensional lattices

@article{Xun2019PreciseBP,
  title={Precise bond percolation thresholds on several four-dimensional lattices},
  author={Zhipeng Xun and Robert M. Ziff},
  journal={Physical Review Research},
  year={2019}
}

• Z. Xun, R. Ziff
• Published 24 October 2019
• Physics
• Physical Review Research

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 $p_c = 0.1601312(2)$, which confirms previous results (based on other methods), and find a new value $p_c=0.035827(1)$ for the SC-NN+2NN lattice, which was not studied previously for bond percolation. For the 4D BCC and FCC lattices, we obtain $p_c=0.074212(1)$ and 0.049517(1), which are substantially more precise than previous values. We also find critical exponents $\tau = 2.3135(5)$ and $\Omega = 0.40(3)$, consistent with previous numerical results and the recent four-loop series result of Gracey [Phys. Rev. D 92, 025012, (2015)].