Finite-size effects for anisotropic bootstrap percolation: logarithmic corrections

Finite size scaling in three-dimensional bootstrap percolation

We consider the problem of bootstrap percolation on a three dimensional lattice and we study its finite size scaling behavior. Bootstrap percolation is an example of Cellular Automata defined on the d-dimensional lattice {1, 2, ..., L} in which each site can be empty or occupied by a single particle; in the starting configuration each site is occupied with probability p, occupied sites remain o...

Finite Size Scaling in Three-Dimensional Bootstrap Percolation

Logarithmic Corrections for Spin Glasses, Percolation and Lee-Yang Singularities in Six Dimensions

We study analytically the logarithmic corrections for the correlation length, susceptibility and specific heat in temperature as well as in the lattice size, for a generic φ3 theory at its upper critical dimension (six). We have also computed the leading correction to the scaling as a function of the lattice size. We distinguish the obtained formulas to the following special cases: percolation,...

Line Percolation in Finite Projective Planes

We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes. We present sharp results on the size of the minimum percolating sets and the maximal non-percolating sets. Additional results on the minimal and maximal percolation time as well as on the critical probability in the projective plane are also presented.

The time of graph bootstrap percolation

Abstract: Graph bootstrap percolation, introduced by Bollobás in 1968, is a cellular automaton defined as follows. Given a “small” graph H and a “large” graph G = G0 ⊆ Kn, in consecutive steps we obtain Gt+1 from Gt by adding to it all new edges e such that Gt ∪ e contains a new copy of H. We say that G percolates if for some t ≥ 0, we have Gt = Kn. ForH = Kr, the question about the size of the...