# 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} }

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…

## 12 Citations

### Bond percolation on simple cubic lattices with extended neighborhoods.

- PhysicsPhysical review. E
- 2020

The results show that the percolation thresholds of these and other three-dimensional lattices decrease monotonically with the coordination number z quite accurately according to a power-law p_{c}∼z^{-a} with exponent a=1.111.

### Site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in two and three dimensions.

- PhysicsPhysical review. E
- 2022

Extended-range percolation on various regular lattices, including all 11 Archimedean lattices in two dimensions and the simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc)…

### Site and bond percolation on four-dimensional simple hypercubic lattices with extended neighborhoods

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

The asymptotic behavior of the percolation threshold p c and its dependence upon coordination number z is investigated for both site and bond percolation on four-dimensional lattices with compact…

### Site percolation thresholds on triangular lattice with complex neighborhoods.

- Computer Science, PhysicsChaos
- 2020

A fast Monte Carlo algorithm is used for determining thresholds pc for random site percolation on a triangular lattice for neighborhoods containing nearest (NN), next-nearest (2NN, next-next-Nearest (3NN), and next-Next-next -next-ne nearest (4NN) neighbors, and their combinations forming regular hexagons.

### Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit.

- PhysicsPhysical review. E
- 2021

By means of extensive Monte Carlo simulation, extended-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors up to the eighth nearest neighbors for the square lattice and the ninth nearestNeighborhoods are found using a single-cluster growth algorithm.

### Critical exponents and universal excess cluster number of percolation in four and five dimensions

- Physics
- 2020

### What are the limits of universality?

- Physics, MathematicsProceedings of the Royal Society A
- 2022

It is a central prediction of renormalization group theory that the critical behaviours of many statistical mechanics models on Euclidean lattices depend only on the dimension and not on the specific…

### Five-loop renormalization of ϕ3 theory with applications to the Lee-Yang edge singularity and percolation theory

- PhysicsPhysical Review D
- 2021

We apply the method of graphical functions that was recently extended to six dimensions for scalar theories, to φ3 theory and compute the β function, the wave function anomalous dimension as well as…

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