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Simulation of Spin Models in Multicanonical Ensemble with Collective Updates

Sylvain Reynal, H. T. Diep

We propose a Monte Carlo method which performs a random walk in energy space using cluster-like collective updates. By imposing that bond probabilities depend continuously on the microcanonical temperature, we obtain dynamic exponents close to their ideal random walk values. The method proves remarkably powerful when applied to models governed by long-range interactions, where it straightforwardly combines with the efficient Luijten-Bloete cluster algorithm to yield a dramatic reduction in the computation load.We propose a Monte Carlo method which performs a random walk in energy space using cluster-like collective updates. By imposing that bond probabilities depend continuously on the microcanonical temperature, we obtain dynamic exponents close to their ideal random walk values. The method proves remarkably powerful when applied to models governed by long-range interactions, where it straightforwardly combines with the efficient Luijten-Bloete cluster algorithm to yield a dramatic reduction in the computation load.

arXiv:cond-mat/0409529Sep 21, 20040 citations

Monte Carlo Simulation of Spin Models with Long-Range Interactions

Erik Luijten

arXiv:cond-mat/9906219Springer proceedings in physicsJan 1, 20001 citation

Wang-Landau Multibondic Cluster Simulations for Second-Order Phase Transitions

Bernd A. Berg, Wolfhard Janke E

For a second-order phase transition the critical energy range of interest is larger than the energy range covered by a canonical Monte Carlo simulation at the critical temperature. Such an extended energy range can be covered by performing a Wang-Landau recursion for the spectral density followed by a multicanonical simulation with fixed weights. But in the conventional approach one loses the advantage due to cluster algorithms. A cluster version of the Wang-Landau recursion together with a subsequent multibondic simulation improves for 2D and 3D Ising models the efficiency of the conventional Wang-Landau or multicanonical approach by power laws in the lattice size. In our simulations real gains in CPU time reach 2 orders of magnitude.For a second-order phase transition the critical energy range of interest is larger than the energy range covered by a canonical Monte Carlo simulation at the critical temperature. Such an extended energy range can be covered by performing a Wang-Landau recursion for the spectral density followed by a multicanonical simulation with fixed weights. But in the conventional approach one loses the advantage due to cluster algorithms. A cluster version of the Wang-Landau recursion together with a subsequent multibondic simulation improves for 2D and 3D Ising models the efficiency of the conventional Wang-Landau or multicanonical approach by power laws in the lattice size. In our simulations real gains in CPU time reach 2 orders of magnitude.

arXiv:cond-mat/0610647Physical Review LettersJan 22, 200714 citations

Cluster algorithms for anisotropic quantum spin models

Naoki Kawashima

arXiv:cond-mat/9506075Journal of Statistical PhysicsJan 1, 199622 citations

Wang–Landau multibondic cluster approach to simulations of second-order transitions

Bernd A. Berg, Wolfhard Janke E

At second-order phase transitions the critical energy range covered by a canonical Monte Carlo simulation close to the critical temperature is often smaller than the energy range needed for reliable reweighting analyses of certain observables. Such an extended energy range can be covered by performing a Wang–Landau recursion for the spectral density followed by a multicanonical simulation with fixed weights. But in the conventional approach based on local update rules one loses the advantage due to non-local cluster algorithms which are well known to drastically reduce critical slowing down. We develop a cluster version of the Wang–Landau recursion together with a subsequent multibondic simulation and show for 2D and 3D Ising models that the efficiency of the conventional Wang–Landau multicanonical approach can be improved by power laws in the lattice size. In our simulations real gains in CPU time reach two orders of magnitude.At second-order phase transitions the critical energy range covered by a canonical Monte Carlo simulation close to the critical temperature is often smaller than the energy range needed for reliable reweighting analyses of certain observables. Such an extended energy range can be covered by performing a Wang–Landau recursion for the spectral density followed by a multicanonical simulation with fixed weights. But in the conventional approach based on local update rules one loses the advantage due to non-local cluster algorithms which are well known to drastically reduce critical slowing down. We develop a cluster version of the Wang–Landau recursion together with a subsequent multibondic simulation and show for 2D and 3D Ising models that the efficiency of the conventional Wang–Landau multicanonical approach can be improved by power laws in the lattice size. In our simulations real gains in CPU time reach two orders of magnitude.

Physics ProcediaJan 1, 20102 citations

Order-N cluster Monte Carlo method for spin systems with long-range interactions

Kouki Fukui, Synge Todo

arXiv:0802.0272Journal of Computational PhysicsDec 28, 200896 citations

Hybrid multicanonical cluster algorithm for efficient simulations of long-range spin models

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