We measure the critical exponents of two-dimensional and three-dimensional random-site percolation and find excellent agreement with Nienhuis exact results (two-dimensions) and good agreement with other numerical work (three-dimensions). We also measure the correlation length amplitude ratio and...

We present a method for simulating the evolution/decay of Coniglio-Klein clusters in the Ising model. We are able to monitor the growth and eventual decay of these critical clusters for the two-dimensional model. The time, τ, taken for a cluster of size, s, to decay to 0 is found to scale as...

We consider an enlarged phase space of the ±J spin glass which includes the dilute Ising model and the frustrated system. The three orthogonal axes in this space are: (i) The fraction of ferro- to antiferro-magnetic bonds, p; (ii) the ratio of the strengths of the antiferro- to ferromagnetic...

We here relate the occurrence of extreme market shares, close to either 0 or 100%, in the media industry to a percolation phenomenon across the social network of customers. We further discuss the possibility of observing self-organized criticality when customers and cinema producers adjust their...