Critical points of the random cluster model with Newman-Ziff sampling

We present a method for computing transition points of the random cluster model using a generalization of the Newman-Ziff algorithm, a celebrated technique in numerical percolation, to the random cluster model. The new method is straightforward to implement and works for real cluster weight $q>0$. Furthermore, results for an arbitrary number of values of $q$ can be found at once within a single simulation. Because the algorithm used to sweep through bond configurations is identical to that of Newman and Ziff, which was conceived for percolation, the method loses accuracy for large lattices when $q>1$. However, by sampling the critical polynomial, accurate estimates of critical points in two dimensions can be found using relatively small lattice sizes, which we demonstrate here by computing critical points for non-integer values of $q$ on the square lattice, to compare with the exact solution, and on the unsolved non-planar square matching lattice. The latter results would be much more difficult to obtain using other techniques.

Restricted Boltzmann Machine representation for the groundstate and excited states of Kitaev Honeycomb model

In this work, the capability of restricted Boltzmann machines (RBMs) to find solutions for the Kitaev honeycomb model with periodic boundary conditions is investigated. The measured groundstate (GS) energy of the system is compared and, for small lattice sizes (e.g. 3×3 with 18 spinors), shown to agree with the analytically derived value of the energy up to a deviation of 0.09 %. Moreover, the wave-functions we find have 99.89 % overlap with the exact ground state wave-functions. Furthermore, the possibility of realizing anyons in the RBM is discussed and an algorithm is given to build these anyonic excitations and braid them for possible future applications in quantum computation. Using the correspondence between topological field theories in (2+1)d and 2d CFTs, we propose an identification between our RBM states with the Moore-Read state and conformal blocks of the 2 d Ising model.

Obtaining Nanostructured ZnO onto Si Coatings for Optoelectronic Applications via Eco-Friendly Chemical Preparation Routes

Although the research on zinc oxide (ZnO) has a very long history and its applications are almost countless as the publications on this subject are extensive, this semiconductor is still full of resources and continues to offer very interesting results worth publishing or warrants further investigation. The recent years are marked by the development of novel green chemical synthesis routes for semiconductor fabrication in order to reduce the environmental impacts associated with synthesis on one hand and to inhibit/suppress the toxicity and hazards at the end of their lifecycle on the other hand. In this context, this study focused on the development of various kinds of nanostructured ZnO onto Si substrates via chemical route synthesis using both classic solvents and some usual non-toxic beverages to substitute the expensive high purity reagents acquired from specialized providers. To our knowledge, this represents the first systematic study involving common beverages as reagents in order to obtain ZnO coatings onto Si for optoelectronic applications by the Aqueous Chemical Growth (ACG) technique. Moreover, the present study offers comparative information on obtaining nanostructured ZnO coatings with a large variety of bulk and surface morphologies consisting of crystalline nanostructures. It was revealed from X-ray diffraction analysis via Williamson–Hall plots that the resulting wurtzite ZnO has a large crystallite size and small lattice strain. These morphological features resulted in good optical properties, as proved by photoluminescence (PL) measurements even at room temperature (295 K). Good optical properties could be ascribed to complex surface structuring and large surface-to-volume ratios.

Mechanical origin of martensite-like structures in two-dimensional ReS2

Martensite is a needle-shaped microstructure formed by a rapid, diffusionless transformation and significantly affects the mechanical properties of materials. Here, in two-dimensional ReS2 we show that martensite-like domain structures can form via a diffusionless transformation, involving small lattice deformations. By analyzing the strain distribution and topology of the as-grown chemical vapor deposition samples, we find that cooling-induced strain at the ReS2/substrate interface is responsible for the mechanical loading and is essential for martensite-like domain formation. Meanwhile, the effect of cooling rate, flake size and substrate on the microstructures revealed the mechanical origin of the transformation. The strain-induced lattice reconstructions are rationalized and possibly lead to ferroelastic effects. In view of the strong anisotropy in electronic and optical properties in two dimensional materials like ReS2, opportunities exist for strain-correlated micro/nanostructure engineering, which has potential use in next-generation strain-tunable devices.

An insulator becomes a conductor under the quantised, critical field: (The Insuductor)

In the solid state physics, one could imagine that if the lattice constant (a) is increased, then what will be the consequences? According to band theory, as long as one starts with a half-filled band (i.e. one electron per unit cell), then, the system will not change but will remain metallic no matter how the atoms were pulled far apart, that will lead to an absurd. Where, at very large lattice separation, there exists a limit, where the conductor becomes just an array of atoms which implies the delocalisation of the electrons at each atom around their nucleus, Hence, the conductor in this limit tends to be an insulator. The big question now is (Why for large values of the lattice constant that array must be an insulator?).At very small lattice separation, the quantum mechanical tunnelling occurs with perfect transmission coefficient, hence, with perfect delocalisation, which ensures the case of a conductor. At very large lattice separation, the quantum mechanical tunnelling is forbidden with zero transmission coefficient, hence, with zero delocalisation. Hence, the localisation coefficient is perfect, and indeed this is the case of an insulator. At very large lattice separation, the conductor becomes an insulator. Applying the negative, critical potential on the lattice separation region allows the delocalisation coefficient to be perfect due to the qunatisation of the critical potential, then, an insulator becomes a conductor. Therefore, (The Insuductor) is an insulator which converted into a conductor under the quantised, critical field.

RG flows in non-perturbative gauge-Higgs unification II: effective action for the Higgs phase near the quantum phase transition

We construct the zero temperature (no compact dimensions) effective action for an SU(2) Yang–Mills theory in five dimensions, with boundary conditions that reduce the symmetry on the four-dimensional boundary located at the origin to a U(1)-complex scalar system. In order to be sensitive to the Higgs phase, we need to include higher dimensional operators in the effective action, which can be naturally achieved by generating it by expanding the corresponding lattice construction in small lattice spacing, taking the naive continuum limit and then renormalizing. In addition, we build in the effective action non-perturbative information, related to a first order quantum phase transition known to exist. As a result, the effective action acquires a finite cut-off that is low and the fine tuning of the scalar mass is rather mild.

Immature HIV-1 assembles from Gag dimers leaving partial hexamers at lattice edges as potential substrates for proteolytic maturation

The CA (capsid) domain of immature HIV-1 Gag and the adjacent spacer peptide 1 (SP1) play a key role in viral assembly by forming a lattice of CA hexamers, which adapts to viral envelope curvature by incorporating small lattice defects and a large gap at the site of budding. This lattice is stabilized by intrahexameric and interhexameric CA-CA interactions, which are important in regulating viral assembly and maturation. We applied subtomogram averaging and classification to determine the oligomerization state of CA at lattice edges and found that CA forms partial hexamers. These structures reveal the network of interactions formed by CA-SP1 at the lattice edge. We also performed atomistic molecular dynamics simulations of CA-CA interactions stabilizing the immature lattice and partial CA-SP1 helical bundles. Free energy calculations reveal increased propensity for helix-to-coil transitions in partial hexamers compared to complete six-helix bundles. Taken together, these results suggest that the CA dimer is the basic unit of lattice assembly, partial hexamers exist at lattice edges, these are in a helix-coil dynamic equilibrium, and partial helical bundles are more likely to unfold, representing potential sites for HIV-1 maturation initiation.

A comparative study on characterizations and synthesis of pure lead sulfide (PbS) and Ag-doped PbS for photovoltaic applications

In this study, a hydrothermal technique was used to synthesize lead sulfide (PbS) and silver (Ag)-doped PbS nanoparticles (NPs) at different concentrations of 20, 40, and 60% of Ag. The small lattice phase changes appeared due to the shifting of diffraction angle peaks toward higher 2θ for samples doped with PbS with increasing Ag content. The analysis of average crystallite size, phase structure, and lattice constant was observed under X-ray diffraction. The value of crystallite size, volume of the unit cell, and porosity (%) were found to increase with the increasing concentration of Ag NPs in PbS. The pure PbS crystallite size is small compared to Ag-doped PbS. The optical characteristics including absorption spectra of the prepared samples were investigated and confirmed by using scanning electron microscope and UV-Vis spectroscopy. The observation of the composition showed that higher doping concentrations of Ag lead to an increase in particle size. Absorption peaks in the UV-Vis spectra corresponding to pure and 20, 40, and 60% of Ag/PbS were observed at different wavelengths of 368, 369, 371, and 372 nm, respectively. Fourier transformation infrared spectroscopy peaks were found in the vibration mode of the ions due to the increment in Ag doping concentrations. These results indicate the possibility of tuning the optical structural properties of Ag-doped PbS through doping various concentrations of Ag NPs. Ag-doped PbS is considered promising future semiconductor nanomaterial, which will enhance the efficiency of photovoltaic device applications.

High-Rate and Long-Life Cycle of Nano-LiMn2O4 Under High Cut-Off Potential

Nano-LiMn2O4 was successfully synthesized by a low-temperature hydrothermal route with the absence of post-calcination treatment. Employing ethanol as an organic reagent triggers the formation of nanostructured particles approximately 30.39 nm in diameter, associated with 0.7 % lattice strain. The pure phase of nano-LiMn2O4/Li displays outstanding electrochemical performances. Under 4.6 V vs Li+/Li cut-off potential, 74.3 % of capacity is reserved when C-rate is increased by 50 times, while excellent capacity restoration of 96.9 % after cycled again at 1 C. After 331 cycles, capacity retention of 84.3 % is harvested by nano-LiMn2O4/Li, implying the absence of phase transformations in spinel structures under such abuse condition. This remarkable structural stability can be attributed to the small lattice strain, associated with high Li+ diffusion coefficient, which is estimated to be 10-9.76 cm2 s-1 by the EIS technique. Additionally, Li+ extraction is more favourable when nano-LiMn2O4/Li is charged up to 4.6 V vs Li+/Li, interpreted by the polarization resistance (Rp) of the cell.