On the duality relation for correlation functions of the Potts model

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

Multicritical Points of Potts Spin Glasses on the Triangular Lattice

We predict the locations of several multicritical points of the Potts spin glass model on the triangular lattice. In particular, continuous multicritical lines, which consist of multicritical points, are obtained for two types of two-state Potts (i.e., Ising) spin glasses with two- and three-body interactions on the triangular lattice. These results provide us with numerous examples to further verify the validity of the conjecture, which has succeeded in deriving highly precise locations of multicritical points for several spin glass models. The technique, called the direct triangular duality, a variant of the ordinary duality transformation, directly relates the triangular lattice with its dual triangular lattice in conjunction with the replica method.Comment: 18 pages, 2, figure

Extending the Energy Framework for Network Simulator 3 (ns-3)

The problem of designing and simulating optimal transmission protocols for energy harvesting wireless networks has recently received considerable attention, thus requiring for an accurate modeling of the energy harvesting process and a consequent redesign of the simulation framework to include it. While the current ns-3 energy framework allows the definition of new energy sources that incorporate the contribution of an energy harvester, the integration of an energy harvester component into an existing energy source is not straightforward using the existing energy framework. In this poster, we propose an extension of the energy framework currently released with ns-3 in order to explicitly introduce the concept of an energy harvester. Starting from the definition of the general interface, we then provide the implementation of two simple models for the energy harvester. In addition, we extend the set of implementations of the current energy framework to include a model for a supercapacitor energy source and a device energy model for the energy consumption of a sensor. Finally, we introduce the concept of an energy predictor, that gathers information from the energy source and harvester and use this information to predict the amount of energy that will be available in the future, and we provide an example implementation. As a result of these efforts, we believe that our contributions to the ns-3 energy framework will provide a useful tool to enhance the quality of simulations of energy-aware wireless networks.Comment: 2 pages, 4 figures. Poster presented at WNS3 2014, Atlanta, G

Internal Energy of the Potts model on the Triangular Lattice with Two- and Three-body Interactions

We calculate the internal energy of the Potts model on the triangular lattice with two- and three-body interactions at the transition point satisfying certain conditions for coupling constants. The method is a duality transformation. Therefore we have to make assumptions on uniqueness of the transition point and that the transition is of second order. These assumptions have been verified to hold by numerical simulations for q=2, 3 and 4, and our results for the internal energy are expected to be exact in these cases.Comment: 9 pages, 4 figure