CLUSTER VS SINGLE-SPIN ALGORITHMS - WHICH ARE MORE EFFICIENT

A comparison between single-cluster and single-spin algorithms is made for the Ising model in 2 and 3 dimensions. We compare the amount of c omputer time needed to achieve a given level of statistical accuracy, rather than the speed in terms of site updates per second or the dynam ical critical exponents. Our main result is that the cluster algorithm s become more efficient when the system size, L(d), exceeds, L approxi mately 70-300 for d = 2 and l approximately 80-200 for d = 3. The exac t value of the crossover is dependent upon the computer being used. Th e lower end of the crossover range is typical of workstations while th e higher end is typical of vector computers. Hence, even for workstati ons, the system sizes needed for efficient use of the cluster algorith m is relatively large.