45,605 research outputs found
Combinatorial formulation of Ising model revisited
In 1952, Kac and Ward developed a combinatorial formulation for the two
dimensional Ising model which is another method of obtaining Onsager's formula
for the free energy per site in the thermodynamic limit of the model. Feynman
gave an important contribution to this formulation conjecturing a crucial
mathematical relation which completed Kac and Ward ideas. In this paper, the
method of Kac, Ward and Feynman for the free field Ising model in two
dimensions is reviewed in a selfcontained way.Comment: 27 pages, 17 figure
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
On the equivalence of Lambda(t) and gravitationally induced particle production cosmologies
The correspondence between cosmological models powered by a decaying vacuum
energy density and gravitationally induced particle production is investigated.
Although being physically different in the physics behind them we show that
both classes of cosmologies under certain conditions can exhibit the same
dynamic and thermodynamic behavior. Our method is applied to obtain three
specific models that may be described either as Lambda(t)CDM or gravitationally
induced particle creation cosmologies. In the point of view of particle
production models, the later class of cosmologies can be interpreted as a kind
of one-component unification of the dark sector. By using current type Ia
supernovae data, recent estimates of the cosmic microwave background shift
parameter and baryon acoustic oscillations measurements we also perform a
statistical analysis to test the observational viability within the two
equivalent classes of models and we obtain the best-fit of the free parameters.
By adopting the Akaike information criterion we also determine the rank of the
models considered here. Finally, the particle production cosmologies (and the
associated decaying Lambda(t)-models) are modeled in the framework of field
theory by a phenomenological scalar field model.Comment: 9 pages, 3 figures, new comments and 8 references added. Accepted for
publication in Physics Letters
Surviving opinions in Sznajd models on complex networks
The Sznajd model has been largely applied to simulate many sociophysical
phenomena. In this paper we applied the Sznajd model with more than two
opinions on three different network topologies and observed the evolution of
surviving opinions after many interactions among the nodes. As result, we
obtained a scaling law which depends of the network size and the number of
possible opinions. We also observed that this scaling law is not the same for
all network topologies, being quite similar between scale-free networks and
Sznajd networks but different for random networks.Comment: 9 pages, 3 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
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