Growth models on the Bethe lattice

I report on an extensive numerical investigation of various discrete growth models describing equilibrium and nonequilibrium interfaces on a substrate of a finite Bethe lattice. An unusual logarithmic scaling behavior is observed for the nonequilibrium models describing the scaling structure of the infinite dimensional limit of the models in the Kardar-Parisi-Zhang (KPZ) class. This gives rise to the classification of different growing processes on the Bethe lattice in terms of logarithmic scaling exponents which depend on both the model and the coordination number of the underlying lattice. The equilibrium growth model also exhibits a logarithmic temporal scaling but with an ordinary power law scaling behavior with respect to the appropriately defined lattice size. The results may imply that no finite upper critical dimension exists for the KPZ equation.Comment: 5 pages, 5 figure

Critical behavior of the geometrical spin clusters and interfaces in the two-dimensional thermalized bond Ising model

The fractal dimensions and the percolation exponents of the geometrical spin clusters of like sign at criticality, are obtained numerically for an Ising model with temperature-dependent annealed bond dilution, also known as the thermalized bond Ising model (TBIM), in two dimensions. For this purpose, a modified Wolff single-cluster Monte Carlo simulation is used to generate equilibrium spin configurations on square lattices in the critical region. A tie-breaking rule is employed to identify non-intersecting spin cluster boundaries along the edges of the dual lattice. The values obtained for the fractal dimensions of the spanning geometrical clusters $D_{c}$, and their interfaces $D_{I}$, are in perfect agreement with those reported for the standard two-dimensional ferromagnetic Ising model. Furthermore, the variance of the winding angles, results in a diffusivity $\kappa=3$ for the two-dimensional thermalized bond Ising model, thus placing it in the universality class of the regular Ising model. A finite-size scaling analysis of the largest geometrical clusters, results in a reliable estimation of the critical percolation exponents for the geometrical clusters in the limit of an infinite lattice size. The percolation exponents thus obtained, are also found to be consistent with those reported for the regular Ising model. These consistencies are explained in terms of the Fisher renormalization relations, which express the thermodynamic critical exponents of systems with annealed bond dilution in terms of those of the regular model system.Comment: 12 pages, 7 figures, accepted for publication in J. Stat. Mech. (2012

Perovskite Photodiode for Wearable Electronics

Photodetectors are sensing devices that have been used for a broad range electromagnetic wave sensing applications. We are currently investigating the use of photovoltaic cells for implantable and wearable applications [1] [2]. In this work, we have demonstrated the use of CH3NH3PbI3-xClx perovskite materials for photo sensing applications in wearable electronic devices. Our photodetectors were fabricated from two different structures. The first involves the formation of a thin film perovskite material that is sandwiched between bottom and top contact electrodes, while the second involves using hole and electron transport layers between the bottom and top electrodes. Despite a poorer device stability, our experimental results confirmed that devices without an interlayer yield superior performance. Furthermore, AFM results show that the perovskite film formed on top of the PEDOT: PSS layer is non-uniform with more crystalline domains, while it has better surface coverage on top of bare ITO substrates [3] [4]