Thresholds and critical exponents of explosive bond percolation on the square lattice

2021 ◽  
Author(s):  
Qianqian Wu ◽  
Junfeng Wang
Keyword(s):  
Critical Exponents ◽  
Square Lattice ◽  
Bond Percolation

On the time constant and path length of first-passage percolation

1980 ◽  
Vol 12 (04) ◽  
pp. 848-863 ◽  
Author(s):  
Harry Kesten
Keyword(s):  
Distribution Function ◽  
Time Constant ◽  
Path Length ◽  
Passage Time ◽  
Square Lattice ◽  
Bond Percolation ◽  
First Passage Percolation ◽  
Critical Probability ◽  
First Passage ◽  
Individual Bond

Let U be the distribution function of the passage time of an individual bond of the square lattice, and let pT be the critical probability above which the expected size of the open component of the origin (in the usual bond percolation) is infinite. It is shown that if (∗)U(0–) = 0, U(0) < pT , then there exist constants 0 < a, C 1 < ∞ such that a self-avoiding path of at least n steps starting at the origin and with passage time ≦ an} ≦ 2 exp (–C 1 n). From this it follows that under (∗) the time constant μ (U) of first-passage percolation is strictly positive and that for each c > 0 lim sup (1/n)Nn (c) <∞, where Nn (c) is the maximal number of steps in the paths starting at the origin with passage time at most cn.

Fem Based Simulation of Percolation Features of Disordered Heterogeneous Media Elastic Properties

1994 ◽  
Vol 367 ◽  
Author(s):  
S.A. Timan ◽  
V.G. Oshmian
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Critical Exponents ◽  
Heterogeneous Media ◽  
Square Lattice ◽  
Monte Carlo Data ◽  
Disordered System ◽  
Phenomenological Renormalization

AbstractThe mechanical properties of the 2D elastic rigid-nonrigid disordered system in dependence on the concentrations of the rigid phase are studied. The system is constructed on the basis of the square lattice and finite element method (FEM) approximation. The elasticity threshold of the FE system and the critical exponents are detemined by the phenomenological renormalization (PR) of the Monte Carlo data.

Critical Exponents of SAT in Two Dimensional Square Lattice

1999 ◽  
Vol 15 (09) ◽  
pp. 769-774
Author(s):  
Ding En-Yong ◽  
◽  
Huang Yun ◽  
Zhao De-Lu
Keyword(s):  
Critical Exponents ◽  
Square Lattice ◽  
Two Dimensional

QUANTUM MONTE CARLO STUDY OF SITE-DILUTED HEISENBERG ANTIFERROMAGNET ON A SQUARE LATTICE

1999 ◽  
Vol 10 (08) ◽  
pp. 1399-1407 ◽  
Author(s):  
S. TODO ◽  
K. KATO ◽  
H. TAKAYAMA ◽  
K. HARADA ◽  
N. KAWASHIMA ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Critical Exponents ◽  
Quantum Monte Carlo ◽  
Large Scale ◽  
Critical Concentration ◽  
Monte Carlo Study ◽  
Square Lattice ◽  
Heisenberg Antiferromagnet ◽  
Large Systems ◽  
Time Loop

Ground-state phase transition of site-diluted Heisenberg antiferromagnets on a square lattice is studied. By using the continuous-time loop algorithm, we perform large-scale quantum Monte Carlo simulation on large systems at quite low temperatures. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the classical percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. It is found that the transition is not universal, i.e., the critical exponents depend on the spin size S.

Critical sponge dimensions in percolation theory

1981 ◽  
Vol 13 (02) ◽  
pp. 314-324 ◽  
Author(s):  
G. R. Grimmett
Keyword(s):  
Positive Constant ◽  
Percolation Theory ◽  
Square Lattice ◽  
Bond Percolation ◽  
Critical Probability ◽  
Percolation Process ◽  
Open Path ◽  
Image Position

In the bond percolation process on the square lattice, with let S(k) be the probability that some open path joins the longer sides of a sponge with dimensions k by a log k. There exists a positive constant α = αp such that Consequently, the subset of the square lattice {(x, y):0 ≦ y ≦ f(x)} which lies between the curve y = f(x) and the x-axis has the same critical probability as the square lattice itself if and only if f(x)/log x → ∞ as x → ∞.

Sign in / Sign up

Export Citation Format

Share Document