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Multibondic cluster algorithm for finite-size scaling studies of critical phenomena

Bernd A. Berg, Wolfhard Janke E

Computer Physics CommunicationsJan 28, 20081 citation

Cluster algorithms

Ferenc Niedermayer A

arXiv:hep-lat/9704009Springer eBooksApr 7, 20084 citations

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

Framework and properties of cluster algorithms

Werner Kerler A

Nuclear Physics B - Proceedings SupplementsMar 1, 19932 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

Replica-exchange cluster algorithm

Wolfhard Janke E, Elmar Bittner

In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature/energy range around the critical point.By combining the replica-exchange algorithm with cluster updates and an adaptive routine to find the range of interest, we introduce a new flexible and powerful method for systematic investigations of critical phenomena.As a result, we gain two further orders of magnitude in the performance for 2D and 3D Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic algorithm, which is already a great improvement over the standard multicanonical variant.In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature/energy range around the critical point.By combining the replica-exchange algorithm with cluster updates and an adaptive routine to find the range of interest, we introduce a new flexible and powerful method for systematic investigations of critical phenomena.As a result, we gain two further orders of magnitude in the performance for 2D and 3D Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic algorithm, which is already a great improvement over the standard multicanonical variant.

arXiv:1108.0354International Symposium on Lattice Field Theory (LATTICE)Jun 23, 20100 citations

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