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