25,688 research outputs found
Zero-temperature TAP equations for the Ghatak-Sherrington model
The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model
are investigated. The spin-glass energy density (ground state) is determined as
a function of the anisotropy crystal field for a large number of spins.
This allows us to locate a first-order transition between the spin-glass and
paramagnetic phases within a good accuracy. The total number of solutions is
also determined as a function of .Comment: 11 pages, 2 ps figures include
Effects of Random Biquadratic Couplings in a Spin-1 Spin-Glass Model
A spin-1 model, appropriated to study the competition between bilinear
(J_{ij}S_{i}S_{j}) and biquadratic (K_{ij}S_{i}^{2}S_{j}^{2}) random
interactions, both of them with zero mean, is investigated. The interactions
are infinite-ranged and the replica method is employed. Within the
replica-symmetric assumption, the system presents two phases, namely,
paramagnetic and spin-glass, separated by a continuous transition line. The
stability analysis of the replica-symmetric solution yields, besides the usual
instability associated with the spin-glass ordering, a new phase due to the
random biquadratic couplings between the spins.Comment: 16 pages plus 2 ps figure
Finding the optimal nets for self-folding Kirigami
Three-dimensional shells can be synthesized from the spontaneous self-folding
of two-dimensional templates of interconnected panels, called nets. However,
some nets are more likely to self-fold into the desired shell under random
movements. The optimal nets are the ones that maximize the number of vertex
connections, i.e., vertices that have only two of its faces cut away from each
other in the net. Previous methods for finding such nets are based on random
search and thus do not guarantee the optimal solution. Here, we propose a
deterministic procedure. We map the connectivity of the shell into a shell
graph, where the nodes and links of the graph represent the vertices and edges
of the shell, respectively. Identifying the nets that maximize the number of
vertex connections corresponds to finding the set of maximum leaf spanning
trees of the shell graph. This method allows not only to design the
self-assembly of much larger shell structures but also to apply additional
design criteria, as a complete catalog of the maximum leaf spanning trees is
obtained.Comment: 6 pages, 5 figures, Supplemental Material, Source Cod
Fast Community Identification by Hierarchical Growth
A new method for community identification is proposed which is founded on the
analysis of successive neighborhoods, reached through hierarchical growth from
a starting vertex, and on the definition of communities as a subgraph whose
number of inner connections is larger than outer connections. In order to
determine the precision and speed of the method, it is compared with one of the
most popular community identification approaches, namely Girvan and Newman's
algorithm. Although the hierarchical growth method is not as precise as Girvan
and Newman's method, it is potentially faster than most community finding
algorithms.Comment: 6 pages, 5 figure
Wavepacket scattering on graphene edges in the presence of a (pseudo) magnetic field
The scattering of a Gaussian wavepacket in armchair and zigzag graphene edges
is theoretically investigated by numerically solving the time dependent
Schr\"odinger equation for the tight-binding model Hamiltonian. Our theory
allows to investigate scattering in reciprocal space, and depending on the type
of graphene edge we observe scattering within the same valley, or between
different valleys. In the presence of an external magnetic field, the well know
skipping orbits are observed. However, our results demonstrate that in the case
of a pseudo-magnetic field, induced by non-uniform strain, the scattering by an
armchair edge results in a non-propagating edge state.Comment: 8 pages, 7 figure
Hierarchical Spatial Organization of Geographical Networks
In this work we propose the use of a hirarchical extension of the
polygonality index as a means to characterize and model geographical networks:
each node is associated with the spatial position of the nodes, while the edges
of the network are defined by progressive connectivity adjacencies. Through the
analysis of such networks, while relating its topological and geometrical
properties, it is possible to obtain important indications about the
development dynamics of the networks under analysis. The potential of the
methodology is illustrated with respect to synthetic geographical networks.Comment: 3 page, 3 figures. A wokring manuscript: suggestions welcome
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