A comparison between single-cluster and single-spin algorithms is made for the Ising model in 2 and 3 dimensions. We compare the amount of computer time needed to achieve a given level of statistical accuracy, rather ...
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A comparison between single-cluster and single-spin algorithms is made for the Ising model in 2 and 3 dimensions. We compare the amount of computer time needed to achieve a given level of statistical accuracy, rather than the speed in terms of site updates per second or the dynamical critical exponents. Our main result is that the cluster algorithms become more efficient when the system size, L(d), exceeds, L approximately 70-300 for d = 2 and l approximately 80-200 for d = 3. The exact value of the crossover is dependent upon the computer being used. The lower end of the crossover range is typical of workstations while the higher end is typical of vector computers. Hence, even for workstations, the system sizes needed for efficient use of the cluster algorithm is relatively large.
We discuss the loop-algorithm, a new type of cluster algorithm that reduces critical slowing down in vertex models and in quantum spin systems. We cover the example of the 6-vertex model in detail, For the F-model, we...
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We discuss the loop-algorithm, a new type of cluster algorithm that reduces critical slowing down in vertex models and in quantum spin systems. We cover the example of the 6-vertex model in detail, For the F-model, we present numerical results that demonstrate the effectiveness of the loop algorithm. We show how to modify the original algorithm for some more complicated situations, especially for quantum spin systems in one and two dimensions, and we discuss parallelization.
We implemented a parallel Swendsen-Wang algorithm for a 2D Ising system without magnetization in a host-node programming model. The simulations were performed on the Intel Hypercube IPSC/860. Our maximum number of upd...
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We implemented a parallel Swendsen-Wang algorithm for a 2D Ising system without magnetization in a host-node programming model. The simulations were performed on the Intel Hypercube IPSC/860. Our maximum number of updates/s on 32 nodes 1st three times as high as in the implementation by Stauffer and Kertesz on the same machine. With 32 processors we reach half the speed of the simulations by Tamayo and Flanigan on 256 nodes of a CM5. We discuss the non-equilibrium relaxation for the energy and the magnetization.
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.
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