Monte Carlo simulations: Hidden errors from ‘‘good’’ random number generators
Abstract
The Wolff algorithm is now accepted as the best cluster-flipping Monte Carlo algorithm for beating ``critical slowing down.'' We show how this method can yield incorrect answers due to subtle correlations in ``high quality'' random number generators.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
A.M. Ferrenberg et al. identified hidden systematic errors in Monte Carlo simulations when using PRNGs such as CONG, R250, R1279, SWC and SWCW; these generators passed standard statistical randomness tests but exhibited hidden correlations and significant biases in real-world simulations.
“A.M. Ferrenberg et al.15 identified hidden systematic errors in Monte Carlo simulations when using Pseudo Random Number Generators (PRNGs), such as CONG, R250, R1279, SWC and SWCW. Although these generators successfully passed standard statistical randomness tests, they exhibited hidden correlations and significant biases when applied to real-world simulations.”
Cites
Nonuniversal critical dynamics in Monte Carlo simulations
Swendsen, R. H., & Wang, J. (1987) · Physical Review Letters · doi:10.1103/physrevlett.58.86 · Cited by 2,869 · see citing works
Collective Monte Carlo Updating for Spin Systems
Ulli Wolff, A. (1989) · Physical Review Letters · doi:10.1103/physrevlett.62.361 · Cited by 2,564 · see citing works
Critical behavior of the three-dimensional Ising model: A high-resolution Monte Carlo study
Ferrenberg, A. M., & Landau, D. P. (1991) · Physical review. B, Condensed matter · doi:10.1103/physrevb.44.5081 · Cited by 788 · see citing works
Self-citationBounded and Inhomogeneous Ising Models. I. Specific-Heat Anomaly of a Finite Lattice
Ferdinand, A. E., & Fisher, M. E. (1969) · Physical Review · doi:10.1103/physrev.185.832 · Cited by 735 · see citing works
RANDOM NUMBERS FALL MAINLY IN THE PLANES
Marsaglia, G. (1968) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.61.1.25 · Cited by 530 · see citing works
A very fast shift-register sequence random number generator
Kirkpatrick, S., & Stoll, E. (1981) · Journal of Computational Physics · doi:10.1016/0021-9991(81)90227-8 · Cited by 254 · see citing works
Finite-size scaling in the three-dimensional Ising model
Barber, M. N., Pearson, R. B., Toussaint, D., & Richardson, J. L. (1985) · Physical review. B, Condensed matter · doi:10.1103/physrevb.32.1720 · Cited by 134 · see citing works
Statistical and systematic errors in Monte Carlo sampling
Ferrenberg, A. M., Landau, D. P., & Binder, K. (1991) · Journal of Statistical Physics · doi:10.1007/bf01029988 · Cited by 97 · see citing works
Self-citationA random number generator for PC's
Marsaglia, G., Narasimhan, B., & Zaman, A. (1990) · Computer Physics Communications · doi:10.1016/0010-4655(90)90033-w · Cited by 95 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Computer Simulation of Liquids
Allen, M. P., & Tildesley, D. J. (2017) · doi:10.1093/oso/9780198803195.001.0001 · Cited by 20,945 · see citing works
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
Matsumoto, M., & Nishimura, T. (1998) · ACM Transactions on Modeling and Computer Simulation · doi:10.1145/272991.272995 · Cited by 5,780 · see citing works
TestU01: A C library for empirical testing of random number generators
L'Ecuyer, P., & Simard, R. (2007) · ACM Transactions on Mathematical Software · doi:10.1145/1268776.1268777 · Cited by 1,014 · see citing works
Quantum random number generators
Herrero-Collantes, M., & García-Escartín, J. C. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.015004 · Cited by 802 · see citing works
Applications of Monte Carlo methods to statistical physics
Binder, K. (1997) · Reports on Progress in Physics · doi:10.1088/0034-4885/60/5/001 · Cited by 645 · see citing works
Quantum Monte Carlo Approaches for Correlated Systems
Becca, F., & Sorella, S. (2017) · doi:10.1017/9781316417041 · Cited by 523 · see citing works
Chen, K., Ferrenberg, A. M., & Landau, D. P. (1993) · Physical review. B, Condensed matter · doi:10.1103/physrevb.48.3249 · Cited by 331 · see citing works
Self-citationIsing universality in three dimensions: a Monte Carlo study
Blöte, H. W. J., Luijten, E., & Heringa, J. R. (1995) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/28/22/007 · Cited by 308 · see citing works
A portable high-quality random number generator for lattice field theory simulations
Lüscher, M. (1994) · Computer Physics Communications · doi:10.1016/0010-4655(94)90232-1 · Cited by 287 · see citing works
Algorithm 806: SPRNG: a scalable library for pseudorandom number generation
Mascagni, M., & Srinivasan, A. (2000) · ACM Transactions on Mathematical Software · doi:10.1145/358407.358427 · Cited by 275 · see citing works
Relevance of accurate Monte Carlo modeling in nuclear medical imaging
Zaidi, H. (1999) · Medical Physics · doi:10.1118/1.598559 · Cited by 279 · see citing works
Uniform random number generation
L’Ecuyer, P. (1994) · Annals of Operations Research · doi:10.1007/bf02136827 · Cited by 268 · see citing works
Amplifying DNA with arbitrary oligonucleotide primers.Preprint
Caetano‐Anollés, G. (1993) · Genome Research · doi:10.1101/gr.3.2.85 · Cited by 261 · see citing works
Logistic map: A possible random-number generator
Phatak, S. C., & Rao, S. S. (1995) · Physical Review E · doi:10.1103/physreve.51.3670 · Cited by 233 · see citing works
Fast physical random number generator using amplified spontaneous emission
Williams, C. R. S., Salevan, J. C., Li, X., Roy, R., & Murphy, T. E. (2010) · Optics Express · doi:10.1364/oe.18.023584 · Cited by 229 · see citing works
Parallel random numbers: as easy as 1, 2, 3
Salmon, J. K., Moraes, M. A., Dror, R. O., & Shaw, D. E. (2011) · Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis · doi:10.1145/2063384.2063405 · Cited by 227 · see citing works
Numerical Methods of Statistics
Monahan, J. F. (2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511812231 · Cited by 202 · see citing works
Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models
Binder, K., & Luijten, E. (2001) · Physics Reports · doi:10.1016/s0370-1573(00)00127-7 · Cited by 197 · see citing works
Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model
Ferrenberg, A. M., Xu, J., & Landau, D. P. (2018) · Physical review. E · doi:10.1103/physreve.97.043301 · Cited by 193 · see citing works
Self-citationRANLUX: A Fortran implementation of the high-quality pseudorandom number generator of Lüscher
James, F. (1994) · Computer Physics Communications · doi:10.1016/0010-4655(94)90233-x · Cited by 192 · see citing works
Exact Distribution of Energies in the Two-Dimensional Ising Model
Beale, P. D. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.78 · Cited by 191 · see citing works
Stipčević, M., & Koç, Ç. K. (2014) · Springer eBooks · doi:10.1007/978-3-319-10683-0_12 · Cited by 193 · see citing works
Ising Universality in Three Dimensions: A Monte Carlo StudyPreprint
Blöte, H. W. J., Luijten, E., & Heringa, J. R. (1995) · Cited by 178 · see citing works
Monte Carlo Studies of Wetting, Interface Localization and Capillary Condensation
Binder, K., Landau, D. P., & Müller, M. (2003) · Journal of Statistical Physics · doi:10.1023/a:1022173600263 · Cited by 173 · see citing works
Self-citationDamage spreading and critical exponents for “model A” Ising dynamics
Grassberger, P. (1995) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(94)00285-2 · Cited by 176 · see citing works
The Chemical Basis of Diatom Morphogenesis
Gordon, R., & Drum, R. W. (1994) · International review of cytology · doi:10.1016/s0074-7696(08)61544-2 · Cited by 160 · see citing works
Verification and planning for stochastic processes with asynchronous events
Younes, H. L. S., & Simmons, R. G. (2004) · Cited by 162 · see citing works
Conductivity exponent and backbone dimension in 2-d percolation
Grassberger, P. (1999) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(98)00435-x · Cited by 155 · see citing works
Persohn, K., & Povinelli, R. J. (2012) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2011.12.006 · Cited by 144 · see citing works
Quantum random-number generator based on a photon-number-resolving detector
Ren, M., Wu, E., Liang, Y., Yi, J., Wu, G., & Zeng, H. (2011) · Physical Review A · doi:10.1103/physreva.83.023820 · Cited by 138 · see citing works
Markov‐chain monte carlo: Some practical implications of theoretical results
Roberts, G. O., & Rosenthal, J. S. (1998) · Canadian Journal of Statistics · doi:10.2307/3315667 · Cited by 138 · see citing works
Is Omega Squared Less Biased? a Comparison of Three Major Effect Size Indices in One-Way Anova
Okada, K. (2013) · Behaviormetrika · doi:10.2333/bhmk.40.129 · Cited by 128 · see citing works
The good, the bad and the user in soft matter simulations
Wong-ekkabut, J., & Karttunen, M. (2016) · Biochimica et Biophysica Acta (BBA) - Biomembranes · doi:10.1016/j.bbamem.2016.02.004 · Cited by 125 · see citing works
Vibrational frequency shift of HF in helium clusters: Quantum simulation and experiment
Blume, D., Lewerenz, M., Huisken, F., & Kaloudis, M. (1996) · The Journal of Chemical Physics · doi:10.1063/1.472648 · Cited by 125 · see citing works
Semiconductor spin noise spectroscopy: Fundamentals, accomplishments, and challenges
Müller, G. M., Oestreich, M., Römer, M., & Hübner, J. (2010) · Physica E Low-dimensional Systems and Nanostructures · doi:10.1016/j.physe.2010.08.010 · Cited by 117 · see citing works
Physical Tests for Random Numbers in Simulations
Vattulainen, I., Ala-Nissilä, T., & Kankaala, K. (1994) · Physical Review Letters · doi:10.1103/physrevlett.73.2513 · Cited by 110 · see citing works
Ultra-Efficient (Embedded) SOC Architectures based on Probabilistic CMOS (PCMOS) Technology
Chakrapani, L. N., Akgul, B. E. S., Cheemalavagu, S., Korkmaz, P., Palem, K. V., & Seshasayee, B. (2006) · Design, Automation, and Test in Europe · doi:10.1109/date.2006.243978 · Cited by 109 · see citing works
Kobayashi, H., Mark, B. L., & Turin, W. (2012) · CERN Document Server (European Organization for Nuclear Research) · Cited by 101 · see citing works
Testing parallel random number generators
Srinivasan, A., Mascagni, M., & Ceperley, D. M. (2003) · Parallel Computing · doi:10.1016/s0167-8191(02)00163-1 · Cited by 98 · see citing works
Random Number Generators for Parallel Computers
Coddington, P. D. (1997) · Syracuse University Libraries (Syracuse University) · Cited by 96 · see citing works
Computer simulation studies of critical phenomena
Landau, D. P. (1994) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(94)90490-1 · Cited by 96 · see citing works
Self-citation6 Gbps real-time optical quantum random number generator based on vacuum fluctuation
Zheng, Z., Zhang, Y., Huang, W., Yu, S., & Guo, H. M. (2019) · Review of Scientific Instruments · doi:10.1063/1.5078547 · Cited by 95 · see citing works
New Developments in Uniform Pseudorandom Number and Vector Generation
Niederreiter, H. (1995) · Lecture notes in statistics · doi:10.1007/978-1-4612-2552-2_5 · Cited by 90 · see citing works
Resolution of 100 photons and quantum generation of unbiased random numbers
Eaton, M., Hossameldin, A., Birrittella, R. J., Alsing, P. M., Gerry, C. C., Dong, H., Cuevas, C., & Pfister, O. (2022) · Nature Photonics · doi:10.1038/s41566-022-01105-9 · Cited by 88 · see citing works
A Vulnerability in Popular Molecular Dynamics Packages Concerning Langevin and Andersen Dynamics
Cerutti, D. S., Duke, R. E., Freddolino, L., Fan, H., & Lybrand, T. P. (2008) · Journal of Chemical Theory and Computation · doi:10.1021/ct8002173 · Cited by 87 · see citing works
Computing with Very Weak Random Sources
Srinivasan, A., & Zuckerman, D. (1999) · SIAM Journal on Computing · doi:10.1137/s009753979630091x · Cited by 85 · see citing works
MONTE CARLO STUDIES OF THE THREE-DIMENSIONAL ISING MODEL IN EQUILIBRIUM
Martin Hasenbusch, B. (2001) · International Journal of Modern Physics C · doi:10.1142/s0129183101002383 · Cited by 84 · see citing works
A package of Linux scripts for the parallelization of Monte Carlo simulations
Badal, A., & Sempau, J. (2006) · Computer Physics Communications · doi:10.1016/j.cpc.2006.05.009 · Cited by 79 · see citing works
640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser
Zhang, L., Pan, B., Chen, G., Guo, L., Lu, D., Zhao, L., & Wang, W. (2017) · Scientific Reports · doi:10.1038/srep45900 · Cited by 79 · see citing works
Conductivity exponent and backbone dimension in 2-d percolation
Grassberger, P. (1999) · RePEc: Research Papers in Economics · Cited by 79 · see citing works
Physical models as tests of randomness
Vattulainen, I., Ala-Nissilä, T., & Kankaala, K. (1995) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.52.3205 · Cited by 75 · see citing works
Static charges cannot drive a continuous flow of water molecules through a carbon nanotube
Wong-ekkabut, J., Miettinen, M. S., Dias, C. L., & Karttunen, M. (2010) · Nature Nanotechnology · doi:10.1038/nnano.2010.152 · Cited by 75 · see citing works
Quantum technologies in the telecommunications industry
Martin, V., Brito, J. P., Escribano, C., Menchetti, M., White, C., Lord, A., Wissel, F., Gunkel, M., Gavignet, P., Genay, N., et al. (2021) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-021-00108-9 · Cited by 73 · see citing works
Random numbers for large-scale distributed Monte Carlo simulations
Bauke, H., & Mertens, S. (2007) · Physical Review E · doi:10.1103/physreve.75.066701 · Cited by 73 · see citing works
Monte Carlo simulation of 3D self-avoiding walks
Grassberger, P. (1993) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/26/12/017 · Cited by 71 · see citing works
Performance potential for simulating spin models on GPU
Weigel, M. (2011) · Journal of Computational Physics · doi:10.1016/j.jcp.2011.12.008 · Cited by 70 · see citing works
Properties making a chaotic system a good pseudo random number generator
Falcioni, M., Palatella, L., Simone Pigolotti, A., & Vulpiani, A. (2005) · Physical Review E · doi:10.1103/physreve.72.016220 · Cited by 70 · see citing works
A comparative study of some pseudorandom number generators
Vattulainen, I., Kankaala, K., Saarinen, J. P. P., & Ala-Nissilä, T. (1995) · Computer Physics Communications · doi:10.1016/0010-4655(95)00015-8 · Cited by 70 · see citing works
Bad Lattice Structures for Vectors of Nonsuccessive Values Produced by Some Linear Recurrences
L'Ecuyer, P. (1997) · INFORMS journal on computing · doi:10.1287/ijoc.9.1.57 · Cited by 73 · see citing works
Gill, R. D. (1994) · Lecture notes in mathematics · doi:10.1007/bfb0073873 · Cited by 68 · see citing works
On correlations in “good” random number generators
Grassberger, P. (1993) · Physics Letters A · doi:10.1016/0375-9601(93)91122-l · Cited by 65 · see citing works
Probabilistic system-on-a-chip architectures
Chakrapani, L. N., Korkmaz, P., Akgul, B. E. S., & Palem, K. V. (2007) · ACM Transactions on Design Automation of Electronic Systems · doi:10.1145/1255456.1255466 · Cited by 64 · see citing works
Random number generators for massively parallel simulations on GPU
Manssen, M., Weigel, M., & Hartmann, A. K. (2012) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2012-01637-8 · Cited by 64 · see citing works
Review of High-Quality Random Number Generators
James, F., & Moneta, L. (2020) · Computing and Software for Big Science · doi:10.1007/s41781-019-0034-3 · Cited by 62 · see citing works
Parameterizing parallel multiplicative lagged-Fibonacci generators
Mascagni, M., & Srinivasan, A. (2004) · Parallel Computing · doi:10.1016/j.parco.2004.06.001 · Cited by 61 · see citing works
A random number generator based on unpredictable chaotic functions
González, J. A., & Pino, R. (1999) · Computer Physics Communications · doi:10.1016/s0010-4655(99)00233-7 · Cited by 61 · see citing works
Learning from the Past: Approaches for Reproducibility in Computational Neuroscience
Crook, S. M., Davison, A. P., & Pleßer, H. E. (2013) · Springer eBooks · doi:10.1007/978-1-4614-1424-7_4 · Cited by 61 · see citing works
On randomization in sequential and distributed algorithms
Gupta, R., Smolka, S. A., & Bhaskar, S. (1994) · ACM Computing Surveys · doi:10.1145/174666.174667 · Cited by 60 · see citing works
History of uniform random number generation
L’Ecuyer, P. (2017) · Winter Simulation Conference · doi:10.1109/wsc.2017.8247790 · Cited by 62 · see citing works
Real-Time Source-Independent Quantum Random-Number Generator with Squeezed States
Michel, T., Haw, J. Y., Marangon, D. G., Thearle, O., Vallone, G., Villoresi, P., Lam, P. K., & Assad, S. M. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.12.034017 · Cited by 59 · see citing works
Pseudo-random-number generators and the square site percolation threshold
Lee, M. J. (2008) · Physical Review E · doi:10.1103/physreve.78.031131 · Cited by 53 · see citing works
Butler, T. P., Durkan, C., Goulding, D., Slepneva, S., Kelleher, B., Hegarty, S. P., & Huyet, G. (2016) · Optics Letters · doi:10.1364/ol.41.000388 · Cited by 53 · see citing works
On the Periods of Generalized Fibonacci Recurrences
Brent, R. P. (1994) · Mathematics of Computation · doi:10.2307/2153583 · Cited by 52 · see citing works
Casimir effect in critical systems: A Monte Carlo simulation
Krech, M., & Landau, D. P. (1996) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.53.4414 · Cited by 51 · see citing works
Self-citationSaxton, M. J. (2007) · Methods in molecular biology · doi:10.1007/978-1-59745-519-0_20 · Cited by 50 · see citing works
On the Lattice Structure of Certain Linear Congruential Sequences Related to AWC/SWB Generators
Couture, R., & L’Ecuyer, P. (1994) · Mathematics of Computation · doi:10.1090/s0025-5718-1994-1220826-x · Cited by 50 · see citing works
Correlation-powered information engines and the thermodynamics of self-correction
Boyd, A. B., Mandal, D., & Crutchfield, J. P. (2017) · Physical review. E · doi:10.1103/physreve.95.012152 · Cited by 49 · see citing works
A New Two-Dimensional Map with Hidden Attractors
Wang, C., & Ding, Q. (2018) · Entropy · doi:10.3390/e20050322 · Cited by 47 · see citing works
Improving Random Number Generators in the Monte Carlo simulations via twisting and combining
Deng, L.-Y., Guo, R., Lin, D. K. J., & Bai, F. (2007) · Computer Physics Communications · doi:10.1016/j.cpc.2007.10.002 · Cited by 46 · see citing works
Energy, Performance, and Probability Tradeoffs for Energy-Efficient Probabilistic CMOS Circuits
Korkmaz, P., Akgul, B. E. S., & Palem, K. V. (2008) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2008.920139 · Cited by 45 · see citing works
Specific heat of two-dimensional diluted magnets
Selke, W., Николаевич, Щ. Л., & Vasilyev, O. A. (1998) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(98)00274-x · Cited by 45 · see citing works
Gambling with randomness: the use of pseudo-random number generators in GIS
Niel, K. V., & Laffan, S. W. (2003) · International Journal of Geographical Information Systems · doi:10.1080/713811743 · Cited by 45 · see citing works
Pseudo random coins show more heads than tails
Bauke, H., & Mertens, S. (2013) · Cited by 44 · see citing works
Exact solutions to chaotic and stochastic systems
González, J. A., Reyes, L., & Guerrero, L. E. (2001) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.1350455 · Cited by 44 · see citing works
Krech, M., & Landau, D. P. (1999) · Physical review. B, Condensed matter · doi:10.1103/physrevb.60.3375 · Cited by 44 · see citing works
Self-citationMonte Carlo simulation of the ferromagnetic order-disorder transition in a Heisenberg fluid
Nijmeijer, M. J. P., & Weis, J. J. (1996) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.53.591 · Cited by 43 · see citing works
Pseudo Random Coins Show More Heads Than Tails
Bauke, H., & Mertens, S. (2004) · Journal of Statistical Physics · doi:10.1023/b:joss.0000012521.67853.9a · Cited by 42 · see citing works
Long-Term Test of a Fast and Compact Quantum Random Number Generator
Marangon, D. G., Plews, A., Lucamarini, M., Dynes, J. F., Sharpe, A. W., Yuan, Z., & Shields, A. J. (2018) · Journal of Lightwave Technology · doi:10.1109/jlt.2018.2841773 · Cited by 42 · see citing works
Random Number Generators for Parallel Applications
Srinivasan, A., Ceperley, D. M., & Mascagni, M. (1999) · Advances in chemical physics · doi:10.1002/9780470141649.ch2 · Cited by 42 · see citing works
Inversive pseudorandom number generators
Hellekalek, P. (1995) · Winter Simulation Conference · doi:10.1145/224401.224612 · Cited by 41 · see citing works
Operational conditions for random-number generation
Compagner, A. (1995) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.52.5634 · Cited by 41 · see citing works
Barry, T. M. (1996) · Risk Analysis · doi:10.1111/j.1539-6924.1996.tb01439.x · Cited by 41 · see citing works
Pharmacodynamics of meropenem in critically ill patients with febrile neutropenia and bacteraemia
Jaruratanasirikul, S., Limapichat, T., Jullangkoon, M., Aeinlang, N., Ingviya, N., & Wongpoowarak, W. (2011) · International Journal of Antimicrobial Agents · doi:10.1016/j.ijantimicag.2011.04.019 · Cited by 40 · see citing works
On the periods of generalized Fibonacci recurrences
Brent, R. P. (1994) · Mathematics of Computation · doi:10.1090/s0025-5718-1994-1216256-7 · Cited by 40 · see citing works
Probabilistic CMOS Technology: A Survey and Future Directions
Akgul, B. S., Chakrapani, L. N., Korkmaz, P., & Palem, K. V. (2006) · IFIP International Conference on Very Large Scale Integration (VLSI-SoC) · doi:10.1109/vlsisoc.2006.313282 · Cited by 40 · see citing works
Cluster hybrid Monte Carlo simulation algorithms
Plascak, J. A., Ferrenberg, A. M., & Landau, D. P. (2002) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.65.066702 · Cited by 40 · see citing works
Self-citationKim, J.-K., de Souza, A. J. F., & Landau, D. P. (1996) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.54.2291 · Cited by 39 · see citing works
Self-citationDillmann, O., Wolfhard Janke, E., Müller, M., & Binder, K. (2001) · The Journal of Chemical Physics · doi:10.1063/1.1350574 · Cited by 38 · see citing works
A novel dynamic model of pseudo random number generator
Behnia, S., Akhavan, A., Akhshani, A., & Samsudin, A. (2011) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2011.02.006 · Cited by 37 · see citing works
Zhmurov, A. A., Rybnikov, K., Kholodov, Y. A., & Barsegov, V. A. (2010) · The Journal of Physical Chemistry B · doi:10.1021/jp109079t · Cited by 37 · see citing works
- Authors
- Ferrenberg, A. M., Landau, D. P., & Wong, Y. J.
- Affiliations
- University of Georgia (US)
- IBM (United States) (US)
- ORCID
- Landau, D. P.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1992-12-07
- Volume
- 69
- Issue
- 23
- Pages
- 3382-3384
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2090824272
- Cited by
- 437
- References
- 9
- Citations by year
- 2026: 9 · 2025: 3 · 2024: 10 · 2023: 12 · 2022: 5 · 2021: 9 · 2020: 9 · 2019: 12 · 2018: 10 · 2017: 44 · 2016: 5 · 2015: 10 · 2014: 9 · 2013: 9 · 2012: 9
- FWCI
- 11.58
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
- Keywords
- random number generators, Wolff cluster algorithm, critical slowing down
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
