Probabilistic bootstrap percolation
- Univ. of Oxford (United Kingdom)
In bootstrap percolation, sites are occupied with probability p, but those with less than m occupied first neighbors are removed. This culling process is repeated until a stable configuration (all occupied sites have at least m occupied first neighbors or the who lattice is empty) is achieved. For m [ge] m, the transition is first order, while for m < m it is second order, with m-dependent exponents. In probabilistic bootstrap percolation sites have probability r or (1 - r) of being m- or m[prime]-sites, respectively m-sites are those which need at least Bethe lattices, where an exact solution is available. For m = 2 and m[prime] = 3, the transition changes from second to first order at r[sup 1] = 1/2, and the exponent [beta] is different for r < 1/2, r = 1/2, and r > 1/2. The same qualitative behavior is found for m = 1 and m[prime] = 3. On the other hand, for m = 1 and m[prime] = 2 the transition is always second order, with the same exponents of m = 1, for any value of r > 0. We found, for m = z - 1 and m[prime] = z, where z is the coordination number of the lattice, that p[sub c] = 1 for a value of r which depends on z, but is always above zero. Finally, we argue that, for bootstrap percolation on real lattices, the exponents v and [beta] for m = 2 and m = 1 are equal, for dimensions below 6.
- OSTI ID:
- 6652531
- Journal Information:
- Journal of Statistical Physics; (United States), Vol. 70:3-4; ISSN 0022-4715
- Country of Publication:
- United States
- Language:
- English
Similar Records
Ordering and percolation transitions for hard squares: Equilibrium versus nonequilibrium models for adsorbed layers with c(2x2) superlattice ordering
Anharmonic thermal motion of Ag in AgCrSe sub 2 : A high-temperature single-crystal x-ray diffraction study
Related Subjects
CRYSTAL LATTICES
COORDINATION NUMBER
STATISTICAL MODELS
BOOTSTRAP MODEL
CORRELATION FUNCTIONS
MANY-DIMENSIONAL CALCULATIONS
PROBABILITY
RANDOMNESS
COMPOSITE MODELS
CRYSTAL STRUCTURE
FUNCTIONS
MATHEMATICAL MODELS
PARTICLE MODELS
662240* - Models for Strong Interactions- (1992-)