Percolation thresholds, critical exponents, and scaling functions on planar random lattices and their duals

1999 ◽  
Vol 60 (6) ◽  
pp. 6361-6370 ◽  
Author(s):  
H.-P. Hsu ◽  
M.-C. Huang
Keyword(s):  
Critical Exponents ◽  
Scaling Functions ◽  
Random Lattices ◽  
Percolation Thresholds

PERCOLATION THRESHOLDS, CRITICAL EXPONENTS, AND SCALING FUNCTIONS ON SPHERICAL RANDOM LATTICES AND THEIR DUALS

2002 ◽  
Vol 13 (03) ◽  
pp. 383-395
Author(s):  
MING-CHANG HUANG ◽  
HSIAO-PING HSU
Keyword(s):  
Critical Exponents ◽  
Finite Size ◽  
Threshold Concentration ◽  
Width Ratio ◽  
Finite Size Scaling ◽  
Random Lattices ◽  
Regular Lattices ◽  
Universal Values ◽  
Percolation Thresholds ◽  
Percolation Processes

Bond-percolation processes are studied for random lattices on the surface of a sphere, and for their duals. The estimated threshold is 0.3326 ± 0.0005 for spherical random lattices and 0.6680 ± 0.0005 for the duals of spherical random lattices, and the exact threshold is conjectured as 1/3 for two-dimensional random lattices and 2/3 for their duals. A suitably defined spanning probability at the threshold, Ep(pc), for both spherical random lattices and their duals is 0.980±0.005, which may be universal for a 2-d lattice with this spanning definition. The shift-to-width ratio of the distribution function of the threshold concentration and the universal values of the critical value of the effective coordination number can be extended from regular lattices to spherical random lattices and their duals. The results of critical exponents are consistent with the assertion from the universality hypothesis. Finite-size scaling is also examined.

scholarly journals Solution of the explosive percolation quest: Scaling functions and critical exponents

2014 ◽  
Vol 90 (2) ◽  
Author(s):  
R. A. da Costa ◽  
S. N. Dorogovtsev ◽  
A. V. Goltsev ◽  
J. F. F. Mendes
Keyword(s):  
Critical Exponents ◽  
Scaling Functions

Majority-vote model on directed Small-World-Voronoi–Delaunay random lattices

2018 ◽  
Vol 29 (07) ◽  
pp. 1850061
Author(s):  
R. S. C. Brenda ◽  
F. W. S. Lima
Keyword(s):  
Critical Exponents ◽  
Majority Vote ◽  
Small World ◽  
Universality Class ◽  
Two Dimensions ◽  
Critical Properties ◽  
Disordered System ◽  
Vote Model ◽  
Random Lattices ◽  
Second Order Phase Transition

We investigate the critical properties of the nonequilibrium majority-vote model in two-dimensions on directed small-world lattice with quenched connectivity disorder. The disordered system is studied through Monte Carlo simulations: the critical noise ([Formula: see text]), as well as the critical exponents [Formula: see text], [Formula: see text], and [Formula: see text] for several values of the rewiring probability [Formula: see text]. We find that this disordered system does not belong to the same universality class as the regular two-dimensional ferromagnetic model. The majority-vote model on directed small-world lattices presents in fact a second-order phase transition with new critical exponents which do not depend on [Formula: see text] ([Formula: see text]), but agree with the exponents of the equilibrium Ising model on directed small-world Voronoi–Delaunay random lattices.

scholarly journals TWO-LOOP CROSSOVER SCALING FUNCTIONS OF THE O(N) MODEL

2010 ◽  
Vol 25 (29) ◽  
pp. 5349-5368
Author(s):  
DENJOE O'CONNOR ◽  
J. A. SANTIAGO ◽  
C. R. STEPHENS ◽  
A. ZAMORA
Keyword(s):  
Fixed Point ◽  
Equation Of State ◽  
Fixed Points ◽  
Critical Exponents ◽  
Critical Region ◽  
Beta Function ◽  
Scaling Functions ◽  
Running Coupling ◽  
Goldstone Modes ◽  
Renormalization Constants

Using Environmentally Friendly Renormalization, we present an analytic calculation of the series for the renormalization constants that describe the equation of state for the O(N) model in the whole critical region. The solution to the beta-function equation, for the running coupling to order two loops, exhibits crossover between the strong coupling fixed point, associated with the Goldstone modes, and the Wilson–Fisher fixed point. The Wilson functions γλ, γφ and γφ2, and thus the effective critical exponents associated with renormalization of the transverse vertex functions, also exhibit nontrivial crossover between these fixed points.

Sign in / Sign up

Export Citation Format

Share Document