Percolation on a random lattice

Abstract

Using Monte Carlo simulations we study bond percolation on a random two-dimensional lattice. We find that although the critical exponents appear to be the same as for percolation on a regular lattice, the ratio of critical amplitudes, which is also supposed to be universal, is diA'erent.

Results for a critical threshold, the correction-to-scaling exponent and susceptibility amplitude ratio for 2d percolation

“…DMS-0553487. [76] additive polymerization, MC 140(45) 1987 Meir [77] lattice, series 210(10) 1987 Kim, Herrmann, Landau [78] continuum model, MC 14(10) 1987 Nakanishi [79] AB percolation, MC 139(24) 1988 Balberg [80] widthless sticks, MC ≈ 3 1988 Ottavi [81] approx. theory (Gaussian fit) 193.9 1989 Corsten, Jan & Jerrard [82] lattice, MC 75(+40, -25) 1990 S. B. Lee & Torquato [83] penetrable conc.…”

Precision Laboratory Measurements in Nuclear Astrophysics

“…As can be seen in Fig. 35, such an M1 contribution is predicted to be approximately 10% of the 7 Be(p, γ) 8 B cross section [91] measured just below 1 MeV, which yield to a 10% correction of the S 17 -factor extracted from the radiative capture work [92], but not the S 17 factor extracted from the Coulomb Dissociation. Fig.…”

The effect of randomness on the critical behaviour of kinetic gelation

“…From a comparison of the results for the cases of periodic and random initiation we conclude that the randomness of the distribution of initiators is crucial. It is possible that this effect is a more general property of percolation on a random lattice [8] and that the change in amplitude ratio (and possibly exponents) is due to some sort of singular behaviour such as the one found by Griffiths [9]. If this is true, this result is particularly interesting also because for percolation a is less than 0.…”

“…Finite-size scaling plots for periodic initiator placement with cI = 3 x and repulsion distance A = 5 . Corrections to scaling have been removed according to equations(7) and(8). w = 1.6, D=O.3, E = -0.5.…”