Monte Carlo Method with Parallel Computation of Phase Transitions in the Three-Dimensional Ashkin-Teller Model

Musiał, G.; Dębski, L.

doi:10.1007/3-540-48086-2_59

Cited by 10 publications

(5 citation statements)

References 10 publications

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“…These considerations were carried out for a system with a single order parameter. In the paper [9] we have generalized the use of the cumulant V L for a system with many order parameters, like the AT model. To determine the phase transition connected with the order parameter 〈s〉, the moments 〈E n 〉 L in the cumulant (3) should be calculated only for the interactions between spins s (the first term in the Hamiltonian (1)).…”

Section: The Parallelized Monte Carlo Simulationsmentioning

confidence: 99%

Parallel Simulations of the Monte Carlo Type: 3D Ashkin-Teller Model

Musiał

Dębski

Kamieniarz

2007

CMST

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The method of parallelization of processing in simulations of the Monte Carlo type is proposed and tested on the 3D Ashkin-Teller model characterized by a rich phase diagram. The message passing is applied and the MPI library is exploited. It is demonstrated that the method works well in different regions of the phase diagram, where the phase transitions are first-order and continuous. The dependence of speedup and efficiency on the number of parallel processes is studied. The condition for the best speedup and efficiency in these simulations is formulated and discussed using the results obtained on symmetric NUMA multiprocessor and on symmetric multicomputer. The suggestion as to effective use of the method even in highly heterogeneous computer systems is also given.

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Section: The Parallelized Monte Carlo Simulationsmentioning

confidence: 99%

Parallel Simulations of the Monte Carlo Type: 3D Ashkin-Teller Model

Musiał

Dębski

Kamieniarz

2007

CMST

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“…Very often one has to extrapolate the MC simulations results to those of macroscopic ones, which usually means extrapolation to infinity (e.g. [1][2][3][4]). The larger the lattices considered in the simulations, the better the extrapolated result.…”

Section: Introductionmentioning

confidence: 99%

Distributed Processing of the Lattice in Monte Carlo Simulations of the Ising Type Spin Model

Murawski

Musiał

Pawłowski

2015

CMST

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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.

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“…Generally, parallelization of statistical computational procedures (including Monte-Carlo techniques) is based on decomposition of sample on the equal sub-volumes (see e.g. [16]). This approach is valid only for independent random values (RV), because in terms of time series (TS) or stochastic fields (SF) the elements of sample are interdependent.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Simulation of Inhomogeneous Metocean Fields. Part III: High-Performance Parallel Algorithms

Boukhanovsky¹,

Ivanov²

2003

Lecture Notes in Computer Science

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The paper discusses the high-performance parallel algorithms for stochastic simulation of metocean processes and fields. The approaches for parallel representation of sample estimation procedures, linear stochastic systems, Markov chains, periodically correlated processes and inhomogeneous fields are proposed. The speedup of the proposing algorithms is studied in respect to parameters of the models.

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Monte Carlo Method with Parallel Computation of Phase Transitions in the Three-Dimensional Ashkin-Teller Model

Cited by 10 publications

References 10 publications

Parallel Simulations of the Monte Carlo Type: 3D Ashkin-Teller Model

Parallel Simulations of the Monte Carlo Type: 3D Ashkin-Teller Model

Distributed Processing of the Lattice in Monte Carlo Simulations of the Ising Type Spin Model

Stochastic Simulation of Inhomogeneous Metocean Fields. Part III: High-Performance Parallel Algorithms

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