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 $p_c=0.1601312(2)$, 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)].

References in corpus (32)

• A fast Monte Carlo algorithm for site or bond percolation
• Efficient Monte Carlo algorithm and high-precision results for percolation
• Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices
• Bond and Site Percolation in Three Dimensions
• Universal Formulae for Percolation Thresholds
• Simultaneous analysis of three-dimensional percolation models
• Square lattice site percolation at increasing ranges of neighbor interactions
• Exact Site Percolation Thresholds Using the Site-to-Bond and Star-Triangle Transformations
• Critical Percolation in High Dimensions
• Measures of critical exponents in the four dimensional site percolation
• Exact bond percolation thresholds in two dimensions
• Simple cubic random-site percolation thresholds for complex neighbourhoods
• Percolation Threshold, Fisher Exponent, and Shortest Path Exponent for 4 and 5 Dimensions
• Calculation of percolation thresholds in high dimensions for fcc, bcc, and diamond lattices
• Correction-to-scaling exponent for two-dimensional percolation
• Percolation Thresholds and Fisher Exponents in Hypercubic Lattices
• Simple cubic random-site percolation thresholds for neighborhoods containing fourth-nearest neighbors
• Percolation of overlapping squares or cubes on a lattice
• Simulation of percolation on massively-parallel computers
• Spreading with immunization in high dimensions
• Efficient space virtualisation for Hoshen--Kopelman algorithm
• Effect of Dimensionality on the Percolation Thresholds of Various $d$-Dimensional Lattices
• Universal Finite-Size Scaling for Percolation Theory in High Dimensions
• Site percolation and random walks on d-dimensional Kagome lattices
• Renormalization group for link percolation on planar hyperbolic manifolds
• Series Expansion of the Percolation Threshold on Hypercubic Lattices
• Percolation in a distorted square lattice
• Percolation phase transition by removal of $k^2$-mers from fully occupied lattices
• Universal features of cluster numbers in percolation
• On entropy, specific heat, susceptibility and Rushbrooke inequality in percolation
• Critical p=1/2 in percolation on semi-infinite strips
• Sequential disruption of the shortest path in critical percolation

Cited by in corpus (16)

• Percolation on complex networks: Theory and application
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit
• Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions
• Critical polynomials in the nonplanar and continuum percolation models
• Bond percolation on simple cubic lattices with extended neighborhoods
• Site percolation thresholds on triangular lattice with complex neighborhoods
• Loss-tolerant architecture for quantum computing with quantum emitters
• Critical exponents and universal excess cluster number of percolation in four and five dimensions
• $N$-cluster correlations in four- and five-dimensional percolation
• Site and bond percolation on four-dimensional simple hypercubic lattices with extended neighborhoods
• Percolation thresholds on high dimensional $D_n$ and dense packing lattices
• What are the limits of universality?
• On the monotonicity of the critical time in the Constrained-degree percolation model
• Fractal depth-first search paths in statistical physics models
• Extended-range percolation in five dimensions