Distributed Processing of the Lattice in Monte Carlo Simulations of the Ising Type Spin Model
Murawski Szymon, Musiał Grzegorz, Pawłowski Grzegorz
Faculty of Physics, A. Mickiewicz University
ul. Umultowska 85, 61-614 Pozna ́ n, Poland
∗E-mail: szymon.murawski@gmail.com
Received:
Received: 06 November 2014; revised: 22 May 2015; accepted: 22 May 2015; published online: 30 June 2015
DOI: 10.12921/cmst.2015.21.03.002
Abstract:
Parallelization of processing in Monte Carlo simulations of the Ising spin system with the lattice distributed in a stripe way is proposed. Message passing is applied and one-sided MPI communication with the MPI memory window is exploited. The 2D Ising spin lattice model is taken for testing purposes. The scalability of processing in our simulations is tested in real-life computing on high performance multicomputers and discussed on the basis of speedup and efficiency. The larger the lattice the better scalability is obtained.
Key words:
classical spin lattice model, distributed processing, high performance computing, Monte Carlo simulations, one-sided MPI communication, parallel processing
References:
[1] G. Musiał, L.D ̨ebski, MonteCarlo methodwithparallelcomputation ofphase transitionsinthe three-dimensionalAshkin-Tellemodel,Lect.Notes inComp. Scie. 2328,535 (2002).
[2] G. Musiał, MonteCarloanalysis ofthetricriticalbehavior ina three-dimensionalsystem witha multicomponent order parameter:
The Ashkin-Teller model,Phys. Rev.B69,024407 (2004).
[3] L.D ̨ebski,G.Musiał,J.Rogiers, A Monte Carlostudy of continuous non-Ising phasetransitions inthe3D Ashkin-Teller Model using
the OpenMosix clusterof LinuxPCs, Lect. Notes in Comp.Scie.3019, 455 (2004).
[4] S.Murawski, K. Kapcia, G.Pawłowski, S.Robaszkiewicz,On thephase diagram of the zero-bandwidth extendedhubbard model with
intersite magneticinteractionsforstrongon-site repulsion limitActa Phys.Polon. A 121,1035(2012).
[5] L.Onsager, Crystal statistics.I.Atwo-dimensionalmodelwith anorder-disorder transition Phys.Rev. 65, 117 (1944).
[6] N. Metropolis,A.Rosenbluth,M.Rosenbluth, A.Teller, E.Teller,Equation ofStateCalculationsby FastComputing Machines,J.
Chem.Phys. 21, 1087 (1953).
[7] D.P. Landau,K. Binder, A Guide to MonteCarlo Simulations inStatisticalPhysics,Cambridge UniversityPress,Cambridge2000[8] R.H.Swendsen,J.-S. Wang, Nonuniversalcritical dynamics inMonteCarlo simulations,Phys. Rev. Lett. 58, 86 (1987)[9] F. Wang,D.P.Landau,Determining thedensity ofstates for classicalstatisticalmodels: A randomwalk algorithmtoproduce a flahistogram, Phys.Rev. E64, 056101 (2001).
[10] W. Prokovef, B.Svistunov,Worm algorithms forclassicalstatisticalmodelsPhys. Rev. Letters 87, 60601 (2001).
[11] H.G.Evertz, W. von derLinden,Simulationsoninfinite-size lattices Phys.Rev. Letters86,5164(2001).
[12] http://www.mpi-forum.org/– MPIForum Home Page.
[13] W. Gropp,E. Lusk,A. Skjellum, UsingMPI –2ndEdition: Portable ParallelProgramming with theMessage-Passing Interface, MIT
Press, Cambridge 1999.
[14] E.F.Vande Velde,Concurrent ScientificComputing,Springer-Verlag,New York 1994.
[15] G. M. Ahmdal, Validityofthe Single ProcessorApproachtoAchieving Large-ScaleComputingCapabilities AFIPSConf. Proc. 30,
483 (1963).
[16] M. Suzuki,Quantum statistical MonteCarlo methods andapplications tospinsystems,J.Stat. Phys. 43,883(1986).
[17] X.Qian, Y.Deng,H. W. J. Blöte, Percolationin oneof qcolorsnear criticality,Phys. Rev.E72,056132 (2005).
[18] S.Murawski,K. Kapcia,G. Pawłowski,S.Robaszkiewicz,Monte Carlostudyof phaseseparationin magneticinsulatorsActaPhys.
Pol. A 127,281(2014).
Parallelization of processing in Monte Carlo simulations of the Ising spin system with the lattice distributed in a stripe way is proposed. Message passing is applied and one-sided MPI communication with the MPI memory window is exploited. The 2D Ising spin lattice model is taken for testing purposes. The scalability of processing in our simulations is tested in real-life computing on high performance multicomputers and discussed on the basis of speedup and efficiency. The larger the lattice the better scalability is obtained.
Key words:
classical spin lattice model, distributed processing, high performance computing, Monte Carlo simulations, one-sided MPI communication, parallel processing
References:
[1] G. Musiał, L.D ̨ebski, MonteCarlo methodwithparallelcomputation ofphase transitionsinthe three-dimensionalAshkin-Tellemodel,Lect.Notes inComp. Scie. 2328,535 (2002).
[2] G. Musiał, MonteCarloanalysis ofthetricriticalbehavior ina three-dimensionalsystem witha multicomponent order parameter:
The Ashkin-Teller model,Phys. Rev.B69,024407 (2004).
[3] L.D ̨ebski,G.Musiał,J.Rogiers, A Monte Carlostudy of continuous non-Ising phasetransitions inthe3D Ashkin-Teller Model using
the OpenMosix clusterof LinuxPCs, Lect. Notes in Comp.Scie.3019, 455 (2004).
[4] S.Murawski, K. Kapcia, G.Pawłowski, S.Robaszkiewicz,On thephase diagram of the zero-bandwidth extendedhubbard model with
intersite magneticinteractionsforstrongon-site repulsion limitActa Phys.Polon. A 121,1035(2012).
[5] L.Onsager, Crystal statistics.I.Atwo-dimensionalmodelwith anorder-disorder transition Phys.Rev. 65, 117 (1944).
[6] N. Metropolis,A.Rosenbluth,M.Rosenbluth, A.Teller, E.Teller,Equation ofStateCalculationsby FastComputing Machines,J.
Chem.Phys. 21, 1087 (1953).
[7] D.P. Landau,K. Binder, A Guide to MonteCarlo Simulations inStatisticalPhysics,Cambridge UniversityPress,Cambridge2000[8] R.H.Swendsen,J.-S. Wang, Nonuniversalcritical dynamics inMonteCarlo simulations,Phys. Rev. Lett. 58, 86 (1987)[9] F. Wang,D.P.Landau,Determining thedensity ofstates for classicalstatisticalmodels: A randomwalk algorithmtoproduce a flahistogram, Phys.Rev. E64, 056101 (2001).
[10] W. Prokovef, B.Svistunov,Worm algorithms forclassicalstatisticalmodelsPhys. Rev. Letters 87, 60601 (2001).
[11] H.G.Evertz, W. von derLinden,Simulationsoninfinite-size lattices Phys.Rev. Letters86,5164(2001).
[12] http://www.mpi-forum.org/– MPIForum Home Page.
[13] W. Gropp,E. Lusk,A. Skjellum, UsingMPI –2ndEdition: Portable ParallelProgramming with theMessage-Passing Interface, MIT
Press, Cambridge 1999.
[14] E.F.Vande Velde,Concurrent ScientificComputing,Springer-Verlag,New York 1994.
[15] G. M. Ahmdal, Validityofthe Single ProcessorApproachtoAchieving Large-ScaleComputingCapabilities AFIPSConf. Proc. 30,
483 (1963).
[16] M. Suzuki,Quantum statistical MonteCarlo methods andapplications tospinsystems,J.Stat. Phys. 43,883(1986).
[17] X.Qian, Y.Deng,H. W. J. Blöte, Percolationin oneof qcolorsnear criticality,Phys. Rev.E72,056132 (2005).
[18] S.Murawski,K. Kapcia,G. Pawłowski,S.Robaszkiewicz,Monte Carlostudyof phaseseparationin magneticinsulatorsActaPhys.
Pol. A 127,281(2014).
