Hybrid cluster identification

I present a hybrid method for the labelling of clusters in two-dimensional lattices, which combines the recursive approach with iterative scanning to reduce the stack size required by the pure recursive technique, while keeping its benefits: single pass and straightforward cluster characterization and percolation detection parallel to the labelling. While the capacity to hold the entire lattice in memory is usually regarded as the major constraint for the applicability of the recursive technique, the required stack size is the real limiting factor. Resorting to recursion only for the transverse direction greatly reduces the recursion depth and therefore the required stack. It also enhances the overall performance of the recursive technique, as is shown by results on a set of uniform random binary lattices and on a set of samples of the Ising model. I also show how this technique may replace the recursive technique in Wolff's cluster algorithm, decreasing the risk of stack overflow and increasing its speed, and the Hoshen–Kopelman algorithm in the Swendsen–Wang cluster algorithm, allowing effortless characterization during generation of the samples and increasing its speed.