Two different algorithms for determining the percolation threshold in bootstrap percolation models are compared. One algorithm is the usual literal bootstrap prescription, whereby each site with less than the required number of neighbours, is removed by a repetitive culling process. The second...

Bootstrap percolation (BP) models are systems where sites are initially randomly occupied. Those sites that do not maintain a suitable local environment of occupied sites are successively removed. This culling process can be identified with a cellular automation. Variations of the local rules...

Although there is now a good measure of agreement between Monte Carlo and high-temperature series expansion estimates for Ising (n = 1) models, published results for the critical temperature from series expansions up to 12th order for the three-dimensional classical Heisenberg (n = 3) and XY (n...

We derive high-temperature series expansions for the free energy and susceptibility of the two-dimensional random-bond Ising model with a symmetric bimodal distribution of two positive coupling strengths J1 and J2 and study the influence of the quenched, random bond-disorder on the critical...

The transmission of order approach enables determination of exact bounds for the zero temperature (T = 0) phase transitions in a family of dilute magnets which exhibit long range order at T = 0 only above a threshold χc that is greater than the usual percolation threshold. The complete...