A Multi-Grid Cluster Labeling Scheme

Number of multi-grid cycles needed to converge as a function of log 2 L for the case of bond percolation (circles) and the Ising model (squares), both at the critical point in two dimensions. The lines are 2 ts to the points. The number of congurations ranges from 100 to 1000 for the dierent values of L. 7 algorithms which have been shown to reduce critical slowing down in many dierent systems (for reviews of cluster algorithms, see refs. [1, 2, 22, 23]). The algorithm could also be used in other applications of component labeling , such as image analysis [9]. As an example, the issue of component labeling is relevant to the next generation of high energy physics experiments, since on-line reconstruction of traces will demand fast labeling algorithms. This problem is being studied, for example, in relation to the design of the Superconducting Supercollider (SSC) detectors [24]. We believe that algorithms of this kind, together with SIMD computers with a simple but eective communication network, will be crucial tools in future studies of critical phenomena and of lattice eld theories in the continuum limit.