A fast algorithm for the Cyber 205 to simulate the 3D Ising model

Bhanot, Gyan; Duke, Dennis W.; Salvador, Román

doi:10.1007/bf01011918

Cited by 66 publications

(20 citation statements)

References 7 publications

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“…is prohibitive both from storage requirement and computational effort, even the latter can be reduced by Boolean operations (since σ x are two valued quantities) and multi spin update [19]. Taking translation invariance within periodic boundary conditions into account only g 0,y is needed, or…”

Section: Methodsmentioning

confidence: 99%

Correlation function in Ising models

Ruge

Zhu²,

Wagner

1994

Physica A: Statistical Mechanics and its Applications

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We simulated the fourier transform of the correlation function of the Ising model in two and three dimensions using a single cluster algorithm with improved estimators. The simulations are in agreement with series expansion and the available exact results in d = 2, which shows, that the cluster algorithm can succesfully be applied for correlations. We show as a further result that our data do not support a hypothesis of Fisher that in any d = 2 lattice the fourier transform of the correlation function depends on the lattice generating function only. In d = 3 our simulation are again in agreement with the results from the series expansion, except for the amplitudes f ± , where we find f + /f − = 2.06(1).

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Section: Methodsmentioning

confidence: 99%

Correlation function in Ising models

Ruge

Zhu²,

Wagner

1994

Physica A: Statistical Mechanics and its Applications

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“…For technical reasons, the spins were discretized to occupy 256 equally spaced orientations in the plane. Furthermore, a variant of multispin coding [14] was used to store 7 (discrete) spins in one word and the lattice was composed of two inter-penetrating sub-lattices. As a consequence, each update of the lattice allows us to update 14 separate samples (or, alternatively, 7 pairs of samples) at the same time.…”

mentioning

confidence: 99%

The four-dimensionalXYspin glass

Jain

1996

J. Phys. A: Math. Gen.

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The nearest-neighbour XY spin glass on a hypercubic lattice in four dimensions is studied by Monte Carlo simulations. A finite-size scaling analysis of the data leads to a finite temperature spin glass transition at T c = 0.95 ± 0.15. The critical exponents are estimated to be ν sg = 0.70 ± 0.10 and η sg = −0.28 ± 0.38. The results imply that the lower critical dimensionality for the XY spin glass is less than four.

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“…We use a multi-spin coding technique [28,29] to simulate a large number of systems simultaneously. Since the FORTRAN compiler on the HITAC S-820/80 computer, we have used, treats 32-bit integers, we can update 32 systems independently.…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

Finite-size effects of dimensional crossover in the quasi-two-dimensional three-state Potts model

Yamagata¹

1995

Physica A: Statistical Mechanics and its Applications

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A nearest neighbour spin pair of the quasi-two-dimensional three-state Potts model interacts with the strength J(> 0) in the xy-plane and with λJ (0 ≤ λ ≪ 1) in the z-axis. The phase transition is of second-order when λ = 0 and is of first-order when λ > 0. The dimensional crossover occurs with a change of the order of the phase transition. We study the finite-size effects of the phenomenon by using a Monte Carlo method with a multi-spin coding technique. The prediction of the finite-size scaling theory is consistent with the Monte Carlo results.

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A fast algorithm for the Cyber 205 to simulate the 3D Ising model

Cited by 66 publications

References 7 publications

Correlation function in Ising models

Correlation function in Ising models

The four-dimensionalXYspin glass

Finite-size effects of dimensional crossover in the quasi-two-dimensional three-state Potts model

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