In the strong coupling limit the partition function of SU(2) gauge theory can be reduced to that of the continuous spin Ising model with nearest neighbour pair-interactions. The random cluster representation of the co...
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In the strong coupling limit the partition function of SU(2) gauge theory can be reduced to that of the continuous spin Ising model with nearest neighbour pair-interactions. The random cluster representation of the continuous spin Ising model in two dimensions is derived through a Fortuin-Kasteleyn transformation, and the properties of the corresponding cluster distribution are analyzed. It is shown that for this model, the magnetic transition is equivalent to the percolation transition of Fortuin-Kasteleyn clusters, using local bond weights. These results are also illustrated by means of numerical simulations. (C) 2000 Elsevier Science B.V. All rights reserved.
We present a simple calculation quantitatively explaining the triplet correlations in the popular shift-register random number generator ''R250'', which were recently observed numerically by Schmid and...
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We present a simple calculation quantitatively explaining the triplet correlations in the popular shift-register random number generator ''R250'', which were recently observed numerically by Schmid and Wilding, and are known from general analysis of this type of generator. Starting from these considerations, we discuss various methods to remove these correlations by combining different shift-register generators. We implement and test a particularly simple and fast version, based on an XOR combination of two independent shift-register generators with different time lags. The results indicate that this generator has much better statistical properties than R250, while being only a factor of two slower. This is consistent with previous analytical considerations and successful applications of this type of generator. The known nine-point correlations still present in the generator are quantitatively understood by our simple arguments.
Autocorrelation times for thermodynamic quantities at T(C) are calculated from Monte Carlo simulations of the site-diluted simple cubic Ising model, using the Swendsen-Wang and wolff cluster algorithms. Our results sh...
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Autocorrelation times for thermodynamic quantities at T(C) are calculated from Monte Carlo simulations of the site-diluted simple cubic Ising model, using the Swendsen-Wang and wolff cluster algorithms. Our results show that for these algorithms the autocorrelation times decrease when reducing the concentration of magnetic sites from 100% down to 40%. This is of crucial importance when estimating static properties of the model, since the variances of these estimators increase with autocorrelation time. The dynamical critical exponents are calculated for both algorithms, observing pronounced finite-size effects in the energy autocorrelation data for the algorithm of wolff. We conclude that, when applied to the dilute Ising model, cluster algorithms become even more effective than local algorithms, for which increasing autocorrelation times are expected.
We describe the architecture of the special purpose processor built to realize in hardware cluster wolff algorithm, which is not hampered by a critical slowing down. The processor simulates two-dimensional Ising-like ...
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We describe the architecture of the special purpose processor built to realize in hardware cluster wolff algorithm, which is not hampered by a critical slowing down. The processor simulates two-dimensional Ising-like spin systems. With minor changes the same very effective architecture, which can be defined as a Memory Machine, can be used to study phase transitions in a wide range of models in two or three dimensions.
Scaling relations of cluster distributions for the wolff algorithm are derived. We found them to be well satisfied for the Ising model in d = 3 dimensions. Using scaling and a parametrization of the cluster distributi...
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Scaling relations of cluster distributions for the wolff algorithm are derived. We found them to be well satisfied for the Ising model in d = 3 dimensions. Using scaling and a parametrization of the cluster distribution. we determine the critical exponent beta/nu = 0.516(6) with moderate effort in computing time.
We present an extensive study of a new Monte Carlo acceleration algorithm introduced by wolff for the Ising model. It differs from the Swendsen-Wang algorithm by growing and flipping single clusters at a random seed. ...
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We present an extensive study of a new Monte Carlo acceleration algorithm introduced by wolff for the Ising model. It differs from the Swendsen-Wang algorithm by growing and flipping single clusters at a random seed. In general, it is more efficient than Swendsen-Wang dynamics ford>2, giving zero critical slowing down in the upper critical dimension. Monte Carlo simulations give dynamical critical exponentsz w=0.33±0.05 and 0.44+0.10 ind=2 and 3, respectively, and numbers consistent withz w=0 ind=4 and mean-field theory. We present scaling arguments which indicate that the wolff mechanism for decorrelation differs substantially from Swendsen-Wang despite the apparent similarities of the two methods.
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