A new random-number generator for multispin Monte Carlo algorithms

We develop a novel multispin coded random number generator algorithm to compute bits equal to 1 with probabilityp. Compared to previously used algorithms, this generator is at least equally fast and allows for an arbitrary accuracy of the computed probability without any significant increase in time. An explicit implementation of the algorithm is given for a Cray-1 vector computer, and the modifications for other machines are discussed. Finally, the algorithm is tested by computing the magnetization of the two-dimensional Ising model. The measured speed of the program is 57 million spin-flips per second. The agreement with theoretical values is found to remain very satisfying even when quite close (∼-0.5%) to the critical temperature.

[1]  John G. Zabolitzky,et al.  Monte Carlo simulation of Ising models by multispin coding on a vector computer , 1984 .

[2]  Scott Kirkpatrick,et al.  A very fast shift-register sequence random number generatorjournal of computational physics , 1981 .

[3]  Gene F. Mazenko,et al.  Dynamic critical exponent z in some two-dimensional models , 1981 .

[4]  Marshall N. Rosenbluth,et al.  Further Results on Monte Carlo Equations of State , 1954 .

[5]  D. Huse.  Simple three-state model with infinitely many phases , 1981 .

[6]  Salvador,et al.  Finite-size scaling and the three-dimensional Ising model. , 1986, Physical review. B, Condensed matter.

[7]  A. Guttmann.  Ising model susceptibility amplitudes. II. Three-dimensional lattices , 1975 .

[8]  M. H. Kalos,et al.  A new multispin coding algorithm for Monte Carlo simulation of the Ising model , 1984 .

[9]  S. F. Reddaway,et al.  A very high speed Monte Carlo simulation on DAP , 1985 .

[10]  Kurt Binder,et al.  Monte Carlo Investigation of Dynamic Critical Phenomena in the Two-Dimensional Kinetic Ising Model , 1973 .

[11]  Andrew Chi-Chih Yao,et al.  The complexity of nonuniform random number generation , 1976 .

[12]  R. Friedberg,et al.  Test of the Monte Carlo Method: Fast Simulation of a Small Ising Lattice , 1970 .

[13]  John L. Richardson,et al.  A Fast Processor for Monte-Carlo Simulation , 1983 .

[14]  Michael Creutz,et al.  Microcanonical Monte Carlo Simulation , 1983 .

[15]  Solomon W. Golomb,et al.  Shift Register Sequences , 1981 .