On the growth of percolation clusters: The effects of time correlations

We discuss the effects of the time correlations in the choice of growth sites for percolation clusters in two dimensions. To this end, we study two well-defined models: (i) FIFO (First-In, First-Out), in which the next-cluster growth site is theoldest, and (ii) FILO (First-In, Last-Out), where the next cluster growth site to be chosen is thenewest. We find that FIFO and FILO have dramatically differentkinetic exponents, even though thestatic exponents are the same (viz., percolation exponents). We find that the percolation thresholdp _c is analogous to the point of a linear polymer, and we develop the corresponding tricritical point scaling relations.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday