arXiv subjects

Zhipeng Xun

Publications and source records attributed to Zhipeng Xun.

6 recordsLinked to original sources

arXiv2023

Extended-range percolation in five dimensions

Percolation on a five-dimensional simple hypercubic (sc(5)) lattice with extended neighborhoods is investigated by means of extensive Monte Carlo simulations, using an effective single-cluster growth algorithm. The critical exponents, including $τ$ and $Ω$, the asymptotic behavior of the threshold $p_c$ and its dependence on coordination number $z$ are investigated. Using the bond and site percolation thresholds $p_c = 0.11817145(3)$ and $0.14079633(4)$ respectively given by Mertens and Moore [Phys. Rev. E 98, 022120 (2018)], we find critical exponents of $τ= 2.4177(3)$, $Ω= 0.27(2)$ through a self-consistent process. The value of $τ$ compares favorably with a recent five-loop renormalization predictions $2.4175(2)$ by Borinsky et al. [Phys. Rev. D 103, 116024 (2021)], the value 2.4180(6) that follows from the work of Zhang et al. [Physica A 580, 126124 (2021)], and the measurement of $2.419(1)$ by Mertens and Moore. We also confirmed the bond threshold, finding $p_c = 0.11817150(5)$. sc(5) lattices with extended neighborhoods up to 7th nearest neighbors are studied for both bond and site percolation. Employing the values of $τ$ and $Ω$ mentioned above, thresholds are found to high precision. For bond percolation, the asymptotic value of $zp_c$ tends to Bethe-lattice behavior ($z p_c \sim 1$), and the finite-$z$ correction is found to be consistent with both and $zp_{c} - 1 \sim a_1 z^{-0.88}$ and $zp_{c} - 1 \sim a_0(3 + \ln z)/z$. For site percolation, the asymptotic analysis is close to the predicted behavior $zp_c \sim 32η_c = 1.742(2)$ for large $z$, where $η_c = 0.05443(7)$ is the continuum percolation threshold of five-dimensional hyperspheres given by Torquato and Jiao [J. Chem. Phys 137, 074106 (2015)]; finite-$z$ corrections are accounted for by taking $p_c \approx c/(z + b)$ with $c=1.722(7)$ and $b=1$.

cond-mat.stat-mech↗

arXiv2022

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

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 extended neighborhoods. Simple hypercubic lattices with neighborhoods up to 9th nearest neighbors are studied to high precision by means of Monte-Carlo simulations based upon a single-cluster growth algorithm. For site percolation, an asymptotic analysis confirms the predicted behavior $zp_c \sim 16 η_c = 2.086$ for large $z$, and finite-size corrections are accounted for by forms $p_c \sim 16 η_c/(z+b)$ and $p_c \sim 1- \exp(-16 η_c/z)$ where $η_c \approx 0.1304$ is the continuum percolation threshold of four-dimensional hyperspheres. For bond percolation, the finite-$z$ correction is found to be consistent with the prediction of Frei and Perkins, $zp_{c} - 1 \sim a_{1} (\ln z)/z$, although the behavior $zp_{c} - 1 \sim a_1 z^{-3/4}$ cannot be ruled out.

cond-mat.stat-mech↗

arXiv2021

Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions

Extended-range percolation on various regular lattices, including all eleven Archimedean lattices in two dimensions, and the simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) lattices in three dimensions, is investigated. In two dimensions, correlations between coordination number $z$ and site thresholds $p_c$ for Archimedean lattices up to 10th nearest neighbors (NN) are seen by plotting $z$ versus $1/p_{c}$ and $z$ versus $-1/\ln(1-p_c)$, using the data of d'Iribarne et al. [J. Phys. A 32:2611, 1999] and others. The results show that all the plots overlap on a line with a slope consistent with the theoretically predicted asymptotic value of $zp_{c} \sim 4 η_c = 4.51235$, where $η_c$ is the continuum threshold for disks. In three dimensions, precise site and bond thresholds for BCC and FCC lattices with 2nd and 3rd NN, and bond thresholds for the SC lattice with up to the 13th NN, are obtained by Monte-Carlo simulations, using an efficient single-cluster growth method. For site percolation, the values of thresholds for different types of lattices with compact neighborhoods also collapse together, and linear fitting is consistent with the predicted value of $zp_{c} \sim 8 η_c = 2.7351$, where $η_c$ is the continuum threshold for spheres. For bond percolation, Bethe-lattice behavior $p_c = 1/(z-1)$ is expected to hold for large $z$, and the finite-$z$ correction is confirmed to satisfy $zp_{c} - 1 \sim a_{1}z^{-x}$, with $x=2/3$ for three dimensions as predicted by Frei and Perkins [Electron. J. Probab. 21:56, 2016] and by Xu et al. [Phys. Rev. E, 103:022127, 2021]. Our analysis indicates that for compact neighborhoods, the asymptotic behavior of $zp_{c}$ is universal, depending only upon the dimension of the system and whether site or bond percolation, but not upon the type of lattice.

cond-mat.stat-mech↗

arXiv2020

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

By means of Monte Carlo simulations, we study long-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors, up to the eighth neighbors for the square lattice and the ninth neighbors for the simple cubic lattice. We find precise thresholds for 23 systems using a single-cluster growth algorithm. Site percolation on lattices with compact neighborhoods can be mapped to problems of lattice percolation of extended shapes, such as disks and spheres, and the thresholds can be related to the continuum thresholds $η_c$ for objects of those shapes. This mapping implies $zp_{c} \sim 4 η_c = 4.51235$ in 2D and $zp_{c} \sim 8 η_c = 2.73512$ in 3D for large $z$ for circular and spherical neighborhoods respectively, where $z$ is the coordination number. Fitting our data to the form $p_c = c/(z+b)$ we find good agreement with $c = 2^d η_c$; the constant $b$ represents a finite-$z$ correction term. We also study power-law fits of the thresholds.

cond-mat.stat-mech↗

arXiv2020

Bond percolation on simple cubic lattices with extended neighborhoods

We study bond percolation on the simple cubic (SC) lattice with various combinations of first, second, third, and fourth nearest-neighbors by Monte Carlo simulation. Using a single-cluster growth algorithm, we find precise values of the bond thresholds. Correlations between percolation thresholds and lattice properties are discussed, and our 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 $p_{c} \sim z^{-a}$, with exponent $a = 1.111$. However, for large $z$, the threshold must approach the Bethe lattice result $p_c = 1/(z-1)$. Fitting our data and data for lattices with additional nearest neighbors, we find $p_c(z-1)=1+1.224 z^{-1/2}$.

cond-mat.dis-nn↗

arXiv2020

Precise bond percolation thresholds on several four-dimensional lattices

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 $τ= 2.3135(5)$ 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)].

cond-mat.dis-nn↗