1,437 research outputs found
Yang-Lee Zeros of the Ising model on Random Graphs of Non Planar Topology
We obtain in a closed form the 1/N^2 contribution to the free energy of the
two Hermitian N\times N random matrix model with non symmetric quartic
potential. From this result, we calculate numerically the Yang-Lee zeros of the
2D Ising model on dynamical random graphs with the topology of a torus up to
n=16 vertices. They are found to be located on the unit circle on the complex
fugacity plane. In order to include contributions of even higher topologies we
calculated analytically the nonperturbative (sum over all genus) partition
function of the model Z_n = \sum_{h=0}^{\infty} \frac{Z_n^{(h)}}{N^{2h}} for
the special cases of N=1,2 and graphs with n\le 20 vertices. Once again the
Yang-Lee zeros are shown numerically to lie on the unit circle on the complex
fugacity plane. Our results thus generalize previous numerical results on
random graphs by going beyond the planar approximation and strongly indicate
that there might be a generalization of the Lee-Yang circle theorem for
dynamical random graphs.Comment: 19 pages, 7 figures ,1 reference and a note added ,To Appear in
Nucl.Phys
Regge gravity on general triangulations
We investigate quantum gravity in four dimensions using the Regge approach on
triangulations of the four-torus with general, non-regular incidence matrices.
We find that the simplicial lattice tends to develop spikes for vertices with
low coordination numbers even for vanishing gravitational coupling. Different
to the regular, hypercubic lattices almost exclusively used in previous
studies, we find now that the observables depend on the measure. Computations
with nonvanishing gravitational coupling still reveal the existence of a region
with well-defined expectation values. However, the phase structure depends on
the triangulation. Even with additional higher- order terms in the action the
critical behavior of the system changes with varying (local) coordination
numbers.Comment: uuencoded postscript file, 16 page
Quantum simulation of non-trivial topology
We propose several designs to simulate quantum many-body systems in manifolds
with a non-trivial topology. The key idea is to create a synthetic lattice
combining real-space and internal degrees of freedom via a suitable use of
induced hoppings. The simplest example is the conversion of an open spin-ladder
into a closed spin-chain with arbitrary boundary conditions. Further
exploitation of the idea leads to the conversion of open chains with internal
degrees of freedom into artificial tori and M\"obius strips of different kinds.
We show that in synthetic lattices the Hubbard model on sharp and scalable
manifolds with non-Euclidean topologies may be realized. We provide a few
examples of the effect that a change of topology can have on quantum systems
amenable to simulation, both at the single-particle and at the many-body level.Comment: 12 pages, 15 figure
Symmetric Interconnection Networks from Cubic Crystal Lattices
Torus networks of moderate degree have been widely used in the supercomputer
industry. Tori are superb when used for executing applications that require
near-neighbor communications. Nevertheless, they are not so good when dealing
with global communications. Hence, typical 3D implementations have evolved to
5D networks, among other reasons, to reduce network distances. Most of these
big systems are mixed-radix tori which are not the best option for minimizing
distances and efficiently using network resources. This paper is focused on
improving the topological properties of these networks.
By using integral matrices to deal with Cayley graphs over Abelian groups, we
have been able to propose and analyze a family of high-dimensional grid-based
interconnection networks. As they are built over -dimensional grids that
induce a regular tiling of the space, these topologies have been denoted
\textsl{lattice graphs}. We will focus on cubic crystal lattices for modeling
symmetric 3D networks. Other higher dimensional networks can be composed over
these graphs, as illustrated in this research. Easy network partitioning can
also take advantage of this network composition operation. Minimal routing
algorithms are also provided for these new topologies. Finally, some practical
issues such as implementability and preliminary performance evaluations have
been addressed
OutFlank Routing: Increasing Throughput in Toroidal Interconnection Networks
We present a new, deadlock-free, routing scheme for toroidal interconnection
networks, called OutFlank Routing (OFR). OFR is an adaptive strategy which
exploits non-minimal links, both in the source and in the destination nodes.
When minimal links are congested, OFR deroutes packets to carefully chosen
intermediate destinations, in order to obtain travel paths which are only an
additive constant longer than the shortest ones. Since routing performance is
very sensitive to changes in the traffic model or in the router parameters, an
accurate discrete-event simulator of the toroidal network has been developed to
empirically validate OFR, by comparing it against other relevant routing
strategies, over a range of typical real-world traffic patterns. On the
16x16x16 (4096 nodes) simulated network OFR exhibits improvements of the
maximum sustained throughput between 14% and 114%, with respect to Adaptive
Bubble Routing.Comment: 9 pages, 5 figures, to be presented at ICPADS 201
A Modified X-Torus Topology for Interconnection Network
The interconnection network is the key components for the communication. The X-Torus topology has been designed in the past. It has been found in the previous design, that the router is not being utilized to their maximum and still there is the scope for adding more links in the topology. In this paper, a new topology has been introduced, based on X-Torus topology by adding extra links with a limited degree of the 6. The performance of the topology has been analyzed using the five traffic patterns that are random, neighbor, bit complements, and hot spot traffic over the factors end to end delay, sink bandwidth and average hop count. An improvement of 62% in terms of latency and 15% in terms of throughput has been observed in the proposed topology. This modified X-Torus topology proves to be a better substitute for X-Torus topology
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