Pablo Tamayo

Single-Cluster Monte Carlo Dynamics for the Ising Model

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 exponentszw=0.33±0.05 and 0.44+0.10 ind=2 and 3, respectively, and numbers consistent withzw=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.

Parallel approaches to short range molecular dynamics simulations

No abstract available

A parallel multigrid algorithm for percolation clusters

A new parallel cluster-finding algorithm is formulated by using multigrid relaxation methods very similar to those used for differential equation solvers. For percolation clusters, this approach drastically reduces critical slowing down relative to local or scan relaxation methods. Numerical studies of scaling properties with system size are presented in the case of the 2D percolation clusters of the Swendsen-Wang Ising dynamics running on the Connection Machine.

A parallel scalable approach to short-range molecular dynamics on the CM-5

Presents a scalable algorithm for short-range molecular dynamics which minimizes interprocessor communications at the expense of a modest computational redundancy. The method combines Verlet neighbor lists with coarse-grained cells. Each processing node is associated with a cubic volume of space and the particles it owns are those initially contained in the volume. Data structures for own and visitor particle coordinates are maintained in each node. Visitors are particles owned by one of the 26 neighboring cells but lying within an interaction range of a face. The Verlet neighbor list includes pointers to own-own and own-visitor interactions. To communicate, each of the 26 neighbor cells sends a corresponding block of particle coordinates using message-passing cells. The algorithms has the numerical properties of the standard serial Verlet method and is efficient for hundreds to thousands of particles per node allowing the simulation of large systems with millions of particles. Preliminary results on the new CM-5 supercomputer are described.<<ETX>>

Properties of metastable ising models evolving under the Swendsen-Wang dynamics

The behavior of the metastable nearest neighbor Ising model governed by Swendsen-Wang dynamics (SW) is investigated ind=2. The results are compared to those obtained in standard Metropolis dynamics. Both the SW and Metropolis systems are observed to decay from the metastable state via the formation of nucleating droplets. Nucleation rates are measured and found to agree with those predicted by classical nucleation theory. The growth rates of the droplets are observed to differ between the two dynamics. In addition, the dynamic critical exponentz is measured in a mean-field (Curie-Weiss) metastable Ising model at the spinodal. It is found that for SW dynamics,z=2. Since this is the same value as that obtained in the Metropolis case, this result shows that SW does not change the dynamical universality class at the spinodal.

Combining renormalization group and multigrid methods

At this conference it is hardly necessary to remind you that faster computers by themselves are unlikely to satisfy our needs for improved methods to simulate quantum field theory. Similarly in statistical physics and optimization theory even «simple» problems such as the Ising spin glass and the travelling salesman defy massive simulations. Brute force is not only unaesthetic, it is inadequate. On the other hand, it is necessary to consider new algorithms that are compatible with the architecture of the new generation of vector supercomputers and massively parallel arrays. The fastest and most efficient computing machinery will require codes with large numbers of independent concurrent computations

Gauge-invariant lattice gas for the microcanonical Ising model

We introduce a lattice gas for particles with discrete momenta (1, 0, −1) and local deterministic microdynamics, which exactly reproduces Creutzs microcanonical algorithm for the ferromagnetic Ising model. However, because of the manifest gauge invariance of our variables, both the Ising ferromagnetic and spin-glass systems share precisely the same dynamics with different initial conditions. Additional conservation laws in the 1D Ising case result in a completely integrable system in the limit of zero or unbounded demon energy cutoff. Numerical investigations of ergodicity are presented for the pure Ising lattice gas in one and two dimensions.

On the Parallelization of CHARMM on the CM-5/5E

We describe a new port of CHARMM to the CM-5 supercomputer. This port is based on the original B-H parallelization of CHARMM[2] for MIMD machines but it has an improved communications library.

Benchmarking High-Performance Computing Systems By Means of Local-Creutz Simulations of the d = 2 Ising Model

We have benchmarked various high-performance com puter systems by means of a code that solves the Ising model in two dimensions. We use a simple and porta ble Fortran implementation of the local-Creutz algo rithm. We compare the wall-clock times needed to per form 250,000 iterations of the algorithm on a lattice of 162 spins, for the Thinking Machines Corporation CM-2, the NEC SX-2, one CRAY Y-MP 4/32 processor, the Alliant FX/2800 with a variable number of proces sors, the IBM 3090-200 VF, an IBM 6000 RISC worksta tion, and a Silicon Graphics Iris workstation.

A fast algorithm to simulate the microcanonical dynamics of the Ising model

We describe a computer program that simulates the microcanonical Ising model at a peak speed of 100 mil lion spin updates per second on a single processor of a Class VII supercomputer. The program is vectorized and multispin coded for lattices of all sizes and dimensions by introducing multiple copies for lattices smaller than 128 on a side. Autocorrelations are measured to monitor the effects of critical slowing down and to calculate dy namical critical exponents.