Lattice Size Research Articles

Critical exponents testing of a random number generator with the Wolff cluster algorithm

Finite-size scaling (FSS) of critical exponents including γ, β and α of 2D Ising models of sizes up to 327682 are studied using the Wolff clustering algorithm and are used to assess the quality of pseudorandom number generators (PRNGs). Critical exponents of PRNGs with quality issues are found to diverge from their theoretical values at large lattice sizes, similar to previous reports that used the Metropolis algorithm to simulate the Ising lattice. Four high-quality PRNGs, including Mersenne Twister, an additive lagged Fibonacci generator, Xorshift and Xorwow are tested and assessed with their FSS behaviors. Dynamic exponent z is also used to assess the quality of the four tested PRNGs and corroborating results are obtained.

Multiscale topology optimization for the design of spatially-varying three-dimensional lattice structure

This paper introduces three dimensional (3D) topology optimization specifically tailored for designing spatially-varying primitive-cubic (CP) type lattice structures. The developed design process consists of three steps: pre-processing, main processing, and post-processing. In the pre-processing step, a surrogate model between lattice geometry variables and effective elasticity tensor is constructed using an artificial neural network. This surrogate model is essential because it enables the quick calculation of the effective elasticity tensor of lattice microstructure. In the subsequent main processing step, multiscale topology optimization is performed. During this step, lattice microstructure size and rotation design variables are optimized together with the macrostructure density design variables. Macrostructures are designed using a well-established three-field density scheme with a SIMP formulation. Formulations for spatially-varying 3D lattice microstructure are newly developed based on a unit quaternion rotation representation scheme. In the final post-processing step, a spatially-varying microstructure is restored using a de-homogenization scheme, newly developed particularly for the primitive-cubic (CP) type 3D lattice structures. The effectiveness and robustness of the proposed formulations are validated through three design examples for the compliance minimization problem. Moreover, a designed lattice structure is fabricated using an additive manufacturing machine.

High-throughput assessment of stability and mechanical properties of medium- and high-entropy carbides: Bridging empirical criteria and ab-initio calculations

This study assesses the effectiveness of empirical stability descriptors — the normalized geometric packing parameter, lattice size difference, electronegativities mismatch, and the convex hull analysis based on information on mutually dissolving components, and ab-initio calculated entropy forming ability (EFA) for high-throughput materials discovery in high-entropy ceramics. A sample containing 53,130 medium and high-entropy carbide combinations from the Materials Project database has been analyzed, comparing solid solutions selected based on empirical descriptors and EFA calculations. The suitability of various electronegativity scales is evaluated, while Automatic FLOW (AFLOW) partial occupation (AFLOW-POCC) and special quasirandom structures (SQS) calculations provide insights into enthalpies, bulk moduli, and lattice parameters. It is shown that local distortions play a role in determining the stability of high-entropy ceramics and estimated lattice parameters, Young’s modulus, fracture toughness, and Vickers hardness by computational and experimental approaches. Our analysis demonstrates the efficacy of density functional theory (DFT) approaches for high-throughput screening and highlights the need for the further exploration of the cocktail effect on high-entropy ceramics’ mechanical properties.

Classical and quantum computing of shear viscosity for (2+1)D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for (2+1)-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density ηs is consistent with a well-known holographic result 14π at several temperatures on a 4×4 honeycomb lattice with the local electric representation truncated at jmax=12. We also find the ratio of the spectral function and frequency ρxy(ω)ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond jmax=12 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including jmax truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

Floquet-Rydberg quantum simulator for confinement in Z2 gauge theories

Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators of lattice gauge theories which, among other goals, aim at improving our understanding on the nonperturbative mechanisms underlying the confinement of quarks. In this work, considering periodically driven arrays of Rydberg atoms in a tweezer ladder geometry, we devise a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a Z2 LGT, in which hardcore bosons/spinless fermions are coupled to dynamical gauge fields. Resorting to an external magnetic field to tune the angular dependence of the Rydberg dipolar interactions, and by a suitable tuning of the driving parameters, we manage to suppress the main gauge-violating terms and show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques. Depending on the lattice size, we present a thorough numerical test of the validity of this scheme using either exact diagonalization or matrix-product-state algorithms for the periodically modulated real-time dynamics. Published by the American Physical Society 2024

Defective MOFs as nano carrier for drug loading with controlled release

Metal-organic frameworks (MOFs) are considered highly promising nanomedicine carriers due to their well-defined structures, high specific surface area and porosity, adjustable pore size, and ease of chemical functionalization. However, traditional MOFs face limitations in lattice size and strong non-covalent interactions between the host and guest, posing significant challenges for high and responsive drug loading. In this study, defect-engineered MOFs (UiO-66-NH2) with uniform mesopores were successfully prepared by reducing ligands and adding modulators. Compared to perfect UiO-66-NH2, the loading capacity of the defective UiO-66-NH2 increased more than twofold. Utilizing phase change material as a trigger for drug release, precise temperature-responsive drug release was accomplished. This offers a novel strategy for MOFs materials in drug delivery and controlled release. This study will aid future efforts in using MOFs for selective drug delivery to cells, particularly in cancer treatment and related fields.

Three-dimensional Heisenberg model with Dzyaloshinskii-Moriya interaction: A Monte Carlo study.

The three-dimensional classical Heisenberg model on a simple cubic lattice with Dzyaloshinskii-Moriya (DM) interactions between nearest-neighbors in all directions has been studied using Monte Carlo simulations. The Metropolis algorithm, combined with single histogram reweighting techniques and finite-size scaling analyses, has been used to obtain the thermodynamic behavior of the system in the thermodynamic limit. Simulations were performed with the same set of interaction parameters for both shifted boundary conditions (SBC) and fluctuating boundary conditions (FBC). Because of an incommensurability caused by the DM interaction, the SBC incorporated a fixed shift angle at the boundary which varies as a function of the DM interaction and lattice size. This SBC method decreases the simulation time significantly, but the distribution of states is somewhat different than that obtained with FBC. The ground state for nonzero DM interaction is a spiral configuration where the spins are restricted to lie in planes perpendicular to the DM vector. We found that this spiral configuration undergoes a conventional second-order phase transition into a disordered, paramagnetic state with the transition temperature being a function of the magnitude of the DM interaction. The limiting case with only DM interaction in the model has also been considered. The critical exponent ν, the critical exponent ratios α/ν, β/ν, γ/ν, as well as the critical temperature T_{c} and fourth-order cumulant of the order parameter U_{4}^{*} at T_{c} have been estimated for different magnitudes of DM interaction. The critical exponents and cumulants at the transition are different from those for the three-dimensional Heisenberg model, but the ratios α/ν, β/ν, γ/ν, U_{4}^{*}/ν are the same, implying that weak universality is valid for all values of DM interaction. Structure factor calculations for particular cases have been performed considering SBC and FBC in the simulations with different lattice sizes at the critical temperatures.

Thermalization dynamics in photonic lattices of different geometries

The statistical mechanical behavior of weakly nonlinear multimoded optical settings has been attracting increased interest over the last few years. The main purpose of this work is to numerically investigate the main factors that affect the thermalization process in photonic lattices. In particular, we find that lattices with identically selected properties (such as temperature, coupling coefficient, lattice size, and excitation conditions) can exhibit very different thermalization dynamics and, thus, thermalization distances. Our investigation is focused on two different two-dimensional lattices: the honeycomb lattice and the triangular lattice. Our numerical results show that, independently of the excitation conditions, the honeycomb lattice always thermalizes faster than the triangular lattice. We mainly explain this behavior by the quasilinear spectrum that promotes wave-mixing in the honeycomb lattice in comparison to the power-like spectrum of the triangular lattice. In addition, we investigate the combined effects of temperature as well as the sign and magnitude of the nonlinearity. Switching either the sign of the Kerr nonlinear coefficient or the sign of the temperature can lead to significant differences in the thermalization dynamics, a phenomenon that can be physically explained in terms of wave instabilities. Larger absolute values of the temperature |T| result in more uniform distributions for the power occupation numbers and faster thermalization speeds. Finally, as expected, increasing the magnitude of the nonlinearity results in accelerated thermalization. Our findings provide valuable insights into optical thermalization in discrete systems, where experimental realization may bring about new possibilities for light manipulation and applications.

Synergetic effects of Al addition on the performance of CoFe2O4 catalyst for hydrogen production and filamentous carbon formation from direct cracking of methane

Improving methane catalytic decomposition process was deemed an effective approach for hydrogen production. Here, a novel catalyst AlxCo1-xFe2O4 with a variable aluminum content was synthesized via a co-precipitation route for the direct cracking of methane. The catalytic activity of AlxCo1-xFe2O4 was performed in a fixed bed reactor at temperature of 800°C and 20 mL/min of fed gas. A sequence of characterizations, including SEM, BET, XRD, XPS, Raman and TGA for fresh and spent catalysts, was exploited to examine the influence of Alx content on the morphology, porosity, structure, chemical composition, and cation distribution of AlxCo1-xFe2O4. As the Alx content increased in AlxCo1-xFe2O4 their morphology became more fractal and decreased in particle size, lattice parameter, lattice size, while their pore surface increased. Further cation re-distributions from octahedral to tetrahedral sites as Fe3+ and Al3+ relocated in the Tetrahedral site and Oxygen lattice decreased as observed from Raman and XPS results. Catalytic activity studies showed that Alx content of 0.6 in AlxCo1-xFe2O4 lead maximum methane conversion up to ∼ 91.10 % and hydrogen formation rate of 1.780 ×10-3 mol H2 g-1 s-1. The catalytic activity behavior was explained in correlation with the characteristics of spent catalysts.

Transmission Electron Microscopic and X-ray Diffraction Based Study of Crystallographic Bibliography Demonstrated on Silver, Copper and Titanium Nanocrystals: State of the Art Statical Review

This statistical review compares the crystallographic structures of functional nanocrystals composed of silver (Ag), copper (Cu) and titanium (Ti) using transmission electron microscopy (TEM) and X-ray diffraction (XRD) analyses. TEM provides high-resolution imaging to directly visualize individual nanoparticles' size, internal shape and crystallinity. Statistical analysis quantifies variations in lattice parameters, crystal structure, size distributions, phase compositions, lattice strains, preferred orientation and lattice volume of these three crystalline nanomaterials. The review highlights the complementary roles of TEM and XRD in comprehensive Ag, Cu and Ti nanocrystalline materials characterization. The crystallographic functional parameters of Ag were 2θ= 38.1° (111), 44.3° (200) and 64.4° (220); for Cu crystal 43.3° (111), 50.4° (200), 74.1° (220), 89.9° (311) and 95.1° (222) and 35.1° (100), 38.4° (002), 40.2° (101), 53.0° (102), 63.0° (103), 70.7° (110), 76.2° (112), 82.3° (201) demonstrated for Ti nanocrystals. The crystallographic predominant plane or Miller indices were also revealed by selected area electron diffraction (SAED) on TEM. The FCC structure of Ag and Cu is shown in larger lattice volumes compared to the HCP structure of Ti and prefer oriented. The degree of crystallinity of Ti, Cu and Ag nanocrystalline materials was observed at 90.0%, 98.0% and 100.0% respectively. This quantitative comparison provides valuable insights into the structural property relationships in these nanocrystals, enabling rational design strategies for optimizing their performance in various functional applications.

Numerical tests of the large charge expansion

We perform Monte-Carlo measurements of two and three-point functions of charged operators in the critical O(2) model in 3 dimensions. Our results are compatible with the predictions of the large charge superfluid effective field theory. To obtain reliable measurements for large values of the charge, we improved the Worm algorithm and devised a measurement scheme which mitigates the uncertainties due to lattice and finite size effects.

Unified scaling for the optimal path length in disordered lattices.

In recent decades, much attention has been focused on the topic of optimal paths in weighted networks due to its broad scientific interest and technological applications. In this work we revisit the problem of the optimal path between two points and focus on the role of the geometry (size and shape) of the embedding lattice, which has received very little attention. This role becomes crucial, for example, in the strong disorder (SD) limit, where the mean length of the optimal path (ℓ[over ¯]_{opt}) for a fixed end-to-end distance r diverges as the lattice size L increases. We propose a unified scaling ansatz for ℓ[over ¯]_{opt} in D-dimensional disordered lattices. Our ansatz introduces two exponents, φ and χ, which respectively characterize the scaling of ℓ[over ¯]_{opt} with r for fixed L, and the scaling of ℓ[over ¯]_{opt} with L for fixed r, both in the SD limit. The ansatz is supported by a comprehensive numerical study of the problem on 2D lattices, yet we also present results in D=3. We show that it unifies well-known results in the strong and weak disorder regimes, including the crossover behavior, but it also reveals novel scaling scenarios not yet addressed. Moreover, it provides relevant insights into the origin of the universal exponents characterizing the scaling of the optimal path in the SD limit. For example, for the fractal dimension of the optimal path in the SD limit, d_{opt}, we find d_{opt}=φ+χ.

Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field.

The very existence of a phase transition for spin glasses in an external magnetic field is controversial, even in high dimensions. We carry out massive simulations of the Ising spin-glass in a field, in six dimensions (which, according to classical-but not generally accepted-field-theoretical studies, is the upper critical dimension). We obtain results compatible with a second-order phase transition and estimate its critical exponents for the simulated lattice sizes. The detailed analysis performed by other authors of the replica symmetric Hamiltonian, under the hypothesis of critical behavior, predicts that the ratio of the renormalized coupling constants remain bounded as the correlation length grows. Our numerical results are in agreement with this expectation.

Lattice variation as a function of concentration and grain size in MgO–NiO solid solution system

The study aimed to understand how changes in crystal's size affect the lattice parameters and crystal structure of Mg1-xNixO solid solution for six X values ranging from x = 0 to x = 1. Mg1-xNixO was synthesized via two different wet-chemical techniques: the sol-gel and the microwave hydrothermal method, both followed by calcination at different temperatures of 673, 873, 1073, 1273 and 1473 K. As annealing caused grain growth, the varied temperature range allowed to examine a wide range of grain sizes. The lattice parameters and x values were determined from XRD (X-ray diffraction) peak positions and intensities respectively. The grain size was evaluated by XRD line profile analysis and supported by SEM (scanning electron microscope) observations. At the temperatures of 673 and 873 K grain size was in the nanometric range and from 1073 K and above grain size was in the micrometric range. A non-monotonic lattice variation versus grain size was found for each concentration. When grain size decreased there was a slight contraction, however for grain size in the nanometric range there was a severe lattice expansion. Both lattice parameter changes were explained by two effects acting together: contraction due to surface stress and expansion due to weakening of the ionic bonding at nanocrystalline particles. In this current research study, the lattice parameter was mapped in two dimensions: concentration and grain size. The findings of this study provided valuable insights into the lattice variation in the MgO–NiO solid solution system.

Crystallographic phase stability of nanocrystalline polymorphs TiO2 by tailoring hydrolysis pH

Nanocrystal TiO2 of high crystallinity (88.72 %) polymorphs have been synthesized by a unique simple route. At a low temperature under a measurable condition with differentiated hydrolysis pH of the reaction. Here titanium isopropoxide (TTIP) is used as a precursor, isopropyl alcohol (IP) is a peptizing agent and hydrolysis medium with variable pH (2.0, 2.5, 3.5, 4.5, 5.5, 7.0, 8.5, 9.5) acts as a promoter or catalyst of the reaction. We observed in the whole powder pattern fitting (WPPF) method, TiO2 consisting of 65.0 % anatase, 68.0 % brookite and 45.0 % rutile phase in weight fraction by tailoring different hydrolysis conditions with predominant crystal plane (101), (111), (110) for the individual polymorph anatase, brookite and rutile. The crystal lattice parameters, crystal structure, volume of the crystal lattice, crystal strain, asymmetry, d-spacing and average crystallite size were also studied for the polymorph. The percent of crystallinity dominating around 54.0 to 89.0 % of the titanium and oxygen atoms are arranged regularly and periodically observed for change in the molar ratio (r) tailoring the polymorph phase stability. TiO2 polymorph followed the blue shift at 319.00 to 336.00 nm and had good stability for the decreasing particle size (11.03 nm). This phenomenon has been revealed by transmission electron microscopy (TEM) into the polymorphs. Selected area electron diffraction (SAED) and nanobeam diffraction (NBD) showed the nanocrystal anatase with the prominent miller indices (101) and interplanar distance of 0.35 nm that was revealed by HR-TEM at the lowest pH. Nano anatase is ultrafine which was confirmed by EDS.

Transferring predictions of formation energy across lattices of increasing size*

In this study, we show the transferability of graph convolutional neural network (GCNN) predictions of the formation energy of the nickel-platinum solid solution alloy across atomic structures of increasing sizes. The original dataset was generated with the large-scale atomic/molecular massively parallel simulator using the second nearest-neighbor modified embedded-atom method empirical interatomic potential. Geometry optimization was performed on the initially randomly generated face centered cubic crystal structures and the formation energy has been calculated at each step of the geometry optimization, with configurations spanning the whole compositional range. Using data from various steps of the geometry optimization, we first trained our open-source, scalable implementation of GCNN called HydraGNN on a lattice of 256 atoms, which accounts well for the short-range interactions. Using this data, we predicted the formation energy for lattices of 864 atoms and 2048 atoms, which resulted in lower-than-expected accuracy due to the long-range interactions present in these larger lattices. We accounted for the long-range interactions by including a small amount of training data representative for those two larger sizes, whereupon the predictions of HydraGNN scaled linearly with the size of the lattice. Therefore, our strategy ensured scalability while reducing significantly the computational cost of training on larger lattice sizes.

The study of physical properties of ternary intermetallic MnXGe (X=Al and Ga) alloys: Via DFT and Monte Carlo simulation

The present work aims to investigate the physical properties of the ternary intermetallic MnXGe (X = Al and Ga) using density functional theory (DFT) and Monte Carlo simulation. The obtained ground state results reveal that MnXGe (X = Al and Ga) are stable in the ferromagnetic phase with a metallic character. The total magnetic moments of bulk structure (2D layer MnXGe(001)) are 2.13μB(2.325μB) and 2.30μB(3.28μB) for MnAlGe and MnGaGe, respectively, with the total moments coming mainly from the Mn atom. The ferromagnetic behavior is confirmed by the obtained density of state at the Fermi level and verified by the Stoner criterion. The mechanical, thermodynamic and transport properties show that the alloys are stable with brittle behavior and exhibit weak thermoelectric efficiency. The Monte Carlo simulation demonstrates that the critical temperatures (TC) are 540 K for MnAlGe(001) and 460 K for MnGaGe(001) with lattice size L = 30.

Exploring Lee-Yang and Fisher zeros in the 2D Ising model through multipoint Padé approximants

We present a numerical calculation of the Lee-Yang and Fisher zeros of the 2D Ising model using multipoint Padé approximants. We perform simulations for the 2D Ising model with ferromagnetic couplings both in the absence and in the presence of a magnetic field using a cluster spin-flip algorithm. We show that it is possible to extract genuine signature of Lee-Yang and Fisher zeros of the theory through the poles of magnetization and specific heat, using the multipoint Padé method. We extract the poles of magnetization using Padé approximants and compare their scaling with known results. We verify the circle theorem associated to the well known behavior of Lee-Yang zeros. We present our finite volume scaling analysis of the zeros done at T=Tc for a few lattice sizes, extracting to a good precision the (combination of) critical exponents βδ. The computation at the critical temperature is performed after the latter has been determined via the study of Fisher zeros, thus extracting both βc and the critical exponent ν. Results already exist for extracting the critical exponents for the Ising model in two and three dimensions making use of Fisher and Lee-Yang zeros. In this work, multipoint Padé is shown to be competitive with this respect and thus a powerful tool to study phase transitions. Published by the American Physical Society 2024

Structural trends and itinerant magnetism of the new cage-structured compound HfMn2Zn20

A new cage-structured compound—HfMn2Zn20—belonging to the AB 2 C 20 (A, B = transition or rare earth metals, and C = Al, Zn, or Cd) family of structures has been synthesized via the self-flux method. The new compound crystallizes in the space group Fd3¯m with lattice parameter a ≈ 14.0543(2) Å (Z = 8) and exhibits non-stoichiometry due to Mn/Zn mixing on the Mn-site and an underoccupied Hf-site. The structure refines to Hf0.93Mn1.63Zn20.37 and follows lattice size trends when compared to other HfM 2Zn20 (M = Fe, Co, and Ni) structures. The magnetic measurements show that this compound displays a modified Curie-Weiss behavior with a transition temperature around 22 K. The magnetization shows no saturation, a small magnetic moment, and near negligible hysteresis, all signs of itinerant magnetism. The Rhodes–Wohlfarth ratio and the spin fluctuation parameters ratio both confirm the itinerant nature of the magnetism in HfMn2Zn20.

Vortex ring beams in nonlinear P T-symmetric systems.

In this paper, we investigate a two-dimensional photonic array featuring a circular shape and an alternating gain and loss pattern. Our analysis revolves around determining the presence and resilience of optical ring modes with varying vorticity values. This investigation is conducted with respect to both the array's length and the strength of the non-Hermitian parameter. For larger values of the array's length, we observe a reduction in the stability domain as the non-Hermitian parameter increases. Interestingly, upon increasing the vorticity of the optical modes, full stability windows emerge for shorter lattice size regime.