56,548 research outputs found
Multi-core computation of transfer matrices for strip lattices in the Potts model
The transfer-matrix technique is a convenient way for studying strip lattices
in the Potts model since the compu- tational costs depend just on the periodic
part of the lattice and not on the whole. However, even when the cost is
reduced, the transfer-matrix technique is still an NP-hard problem since the
time T(|V|, |E|) needed to compute the matrix grows ex- ponentially as a
function of the graph width. In this work, we present a parallel
transfer-matrix implementation that scales performance under multi-core
architectures. The construction of the matrix is based on several repetitions
of the deletion- contraction technique, allowing parallelism suitable to
multi-core machines. Our experimental results show that the multi-core
implementation achieves speedups of 3.7X with p = 4 processors and 5.7X with p
= 8. The efficiency of the implementation lies between 60% and 95%, achieving
the best balance of speedup and efficiency at p = 4 processors for actual
multi-core architectures. The algorithm also takes advantage of the lattice
symmetry, making the transfer matrix computation to run up to 2X faster than
its non-symmetric counterpart and use up to a quarter of the original space
Parallel dynamics and computational complexity of the Bak-Sneppen model
The parallel computational complexity of the Bak-Sneppen evolution model is
studied. It is shown that Bak-Sneppen histories can be generated by a massively
parallel computer in a time that is polylogarithmic in the length of the
history. In this parallel dynamics, histories are built up via a nested
hierarchy of avalanches. Stated in another way, the main result is that the
logical depth of producing a Bak-Sneppen history is exponentially less than the
length of the history. This finding is surprising because the self-organized
critical state of the Bak-Sneppen model has long range correlations in time and
space that appear to imply that the dynamics is sequential and history
dependent. The parallel dynamics for generating Bak-Sneppen histories is
contrasted to standard Bak-Sneppen dynamics. Standard dynamics and an alternate
method for generating histories, conditional dynamics, are both shown to be
related to P-complete natural decision problems implying that they cannot be
efficiently implemented in parallel.Comment: 37 pages, 12 figure
BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices
In this paper the elementary moves of the BFACF-algorithm for lattice
polygons are generalised to elementary moves of BFACF-style algorithms for
lattice polygons in the body-centred (BCC) and face-centred (FCC) cubic
lattices. We prove that the ergodicity classes of these new elementary moves
coincide with the knot types of unrooted polygons in the BCC and FCC lattices
and so expand a similar result for the cubic lattice. Implementations of these
algorithms for knotted polygons using the GAS algorithm produce estimates of
the minimal length of knotted polygons in the BCC and FCC lattices
General Algorithm For Improved Lattice Actions on Parallel Computing Architectures
Quantum field theories underlie all of our understanding of the fundamental
forces of nature. The are relatively few first principles approaches to the
study of quantum field theories [such as quantum chromodynamics (QCD) relevant
to the strong interaction] away from the perturbative (i.e., weak-coupling)
regime. Currently the most common method is the use of Monte Carlo methods on a
hypercubic space-time lattice. These methods consume enormous computing power
for large lattices and it is essential that increasingly efficient algorithms
be developed to perform standard tasks in these lattice calculations. Here we
present a general algorithm for QCD that allows one to put any planar improved
gluonic lattice action onto a parallel computing architecture. High performance
masks for specific actions (including non-planar actions) are also presented.
These algorithms have been successfully employed by us in a variety of lattice
QCD calculations using improved lattice actions on a 128 node Thinking Machines
CM-5.
{\underline{Keywords}}: quantum field theory; quantum chromodynamics;
improved actions; parallel computing algorithms
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