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Stability of the Nagaoka-type ferromagnetic state in a t 2 g orbital system on a cubic lattice
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Quantum many-body calculations using body-centered cubic lattices
It is often computationally advantageous to model space as a discrete set of points forming a lattice grid. This technique is particularly useful for computationally difficult problems such as quantum many-body systems. For reasons of simplicity and familiarity, nearly all quantum many-body calculations have been performed on simple cubic lattices. Since the removal of lattice artifacts is often an important concern, it would be useful to perform calculations using more than one lattice geometry. In this paper we show how to perform quantum many-body calculations using auxiliary-field Monte Carlo simulations on a three-dimensional body-centered cubic (BCC) lattice. As a benchmark test we compute the ground state energy of 33 spin-up and 33 spin-down neutrons in the unitary limit, which is an idealized limit where the interaction range is zero and scattering length is infinite. As a fraction of the free Fermi gas energy E FG , we find that the ground state energy is E 0 /E FG =0.369(2),0.371(2), using two different definitions of the finite-system energy ratio. This is in excellent agreement with recent results obtained on a cubic lattice [He et al., Phys. Rev. A 101, 063615 (2020)]. We find that the computational effort and performance on a BCC lattice is approximately the same as that for a cubic lattice with the same number of lattice points. We discuss how the lattice simulations with different geometries can be used to constrain the size of lattice artifacts in simulations of continuum quantum many-body systems.
Phase Transitions in the Antiferromagnetic Heisenberg Model on a Body-Centered Cubic Lattice with Allowance for the Next-Nearest-Neighbor Interactions
Based on the replica exchange Monte Carlo algorithm and histogram analysis of data, the phase transitions in the three-dimensional antiferromagnetic Heisenberg model on a body-centered cubic lattice with allowance for the next-nearest-neighbor interaction are studied. The study is performed for the nextnearest- neighbor exchange interaction ratio of r = 1. It is established that, for this model, the transition from the antiferromagnetic to paramagnetic phase is a first-order phase transition.
Relativistic LCAO for the cubic lattice. Striking features of photoemission from liquid-nitrogen-cooled silver bromide Quarterly status report
Relativistic approximation for valence bands in cubic lattices, and photoemission changes of silver bromide during cooling
Studying Thermodynamic Properties of the Ising Model on a Body-Centered Cubic Lattice with Competing Exchange Interactions
Using the Monte Carlo method, magnetic structures of the ground state and thermodynamic properties of the antiferromagnetic Ising model on a body-centered cubic lattice with competing exchange interactions are studied. The investigations are carried out for the ratio of the exchange interactions of next and nearest neighbors r = J{sub 2}/J{sub 1} = 2/3. All possible magnetic structures of the ground state for this ratio of exchange interactions have been obtained. It has been shown that at r = 2/3 the competition of exchange interactions does not lead to the appearance of frustration and degeneracy of the ground state. Based on the histogram data analysis, it has been shown that the phase transition of the second kind is observed in the model under study at r = 2/3.
Phase Transitions and the Critical Properties of the Heisenberg Model on a Body-Centered Cubic Lattice
The Monte Carlo replica technique is used to study phase transitions and the thermodynamic and critical properties of the three-dimensional Heisenberg antiferromagnetic model on the body-centered cubic lattice with the inclusion of the interaction of the nearest and the next-nearest neighbors. The studies are performed for the proportions of the values of the exchange interactions of the nearest and the next-nearest neighbors in the range of values of k [0.0, 0.6]. The phase transition character is analyzed based on the histogram method. The overall set of static critical indices is calculated in terms of the theory of the finite-dimensional scaling. It is shown that the class of the critical behavior universality of this model is conserved in the above range of values of k.
Interaction of macroparticles localized in Wigner–Seitz cells of various types of cubic lattices in an equilibrium plasma
The interaction of two charged point macroparticles located in Wigner–Seitz cells of simple cubic (SC), body-centered cubic (BCC), or face-centered cubic (FCC) lattices in an equilibrium plasma has been studied within the Debye approximation or, more specifically, based on the linearized Poisson–Boltzmann model. The shape of the outer boundary is shown to exert a strong influence on the pattern of electrostatic interaction between the two macroparticles, which transforms from repulsion at small interparticle distances to attraction as the interparticle distance approaches half the length of the computational cell. The macroparticle pair interaction potential in an equilibrium plasma is shown to be nevertheless the Debye one and purely repulsive for likely charged macroparticles.
S U ( 2 ) principal chiral model with tensor renormalization group on a cubic lattice
We study the continuous phase transition and thermodynamic observables in the three-dimensional Euclidean S U ( 2 ) principal chiral field model with the triad tensor renormalization group and the anisotropic tensor renormalization group methods. Using these methods, we find results that are consistent with previous Monte Carlo estimates and the predicted renormalization group scaling of the magnetization close to criticality. These results bring us one step closer to studying finite-density quantum chromodynamics in four dimensions using tensor network methods. Published by the American Physical Society 2024
Calculation of body-centered-cubic lattice sums with an application to ferromagnetism.
The lattice sums for the bcc lattice are recalculated using the method of Flax and Raich to obtain more general expressions, valid for all temperatures, in terms of a Langevin function and its derivatives. Formulas are presented which enable easy numerical evaluation. A comparison with well-known low-temperature expansions and with the results of direct numerical integration demonstrates the validity at low temperatures of the more general expressions calculated here.
Barium titanate nanoparticles: Short-range lattice distortions with long-range cubic order
Barium titanate (BTO) nanoparticles (sizes 10 to 500 nm) exhibit a displacement of the Ti atom from the center of the Perovskite unit cell as inferred from synchrotron X-ray diffraction patterns (XRD) analyzed using atomic pair distribution functions (PDFs). Fits to PDFs acquired at temperatures of 20° to 220°C indicate that these Ti displacements (~ 0.1 Å) are comparable to or even greater than those in the bulk material. Moreover, these displacements persist at temperatures well above 120°C where the tetragonal to pseudo-cubic phase transition occurs in the bulk. Tetragonal Raman spectral lines were observed for all sizes of these BTO nanoparticles and confirm a distorted unit cell up to 120°C. Above 120°C, the small BTO nanoparticles (10, 50, 100 nm) continue to display tetragonal Raman lines, though with slowly decreasing amplitudes as the temperature rises. In contrast, the tetragonal Raman lines of large BTO nanoparticles (300, 400, 500 nm) disappear abruptly above 120°C, suggestive of bulk material. Indeed, fits to large-particle X-ray PDFs over the range 20-60 Å reveal a sharp, long-range structural change toward a cubic lattice at 120°C, again consistent with bulk material. This sharp, long-range structural change is absent in the small particles. In fact, laboratory XRD Bragg peak profiles for the small BTO particles appear to be singlets at 20°C, indicating that significant long-range cubic order already exists at room temperature. As temperature rises, this long-range cubic order is gradually reinforced as inferred from long-range fits of the small particle PDFs. By combining information from X-ray PDFs, Raman spectra, and Bragg peak profiles, we conclude that small BTO nanoparticles exhibit both short-range (unit-cell) distortion and long-range (mesoscale) cubic order from 20° to 220°C, while the large nanoparticles behave as bulk material, differing from small particles only by exhibiting long-range tetragonal order below 120°C and a mesoscale structural phase change at 120°C.
Structure of One-Dimensional Rubidium and Silver Iodide Crystals in the Channels of Single-Walled Carbon Nanotubes
The structures of one-dimensional (1D) RbI, AgI, and RbAg{sub 4}I{sub 5} crystals inside single-walled carbon nanotube (SWCNT) channels of 1D crystal@SWCNT nanocomposites formed by the capillary technique have been studied by high-resolution (scanning) transmission electron microscopy and computer modeling. 1D RbI crystals form a cubic lattice in a limited space, while 1D AgI crystals form a hexagonal lattice, as in their ternary compounds. The 1D RbAg{sub 4}I{sub 5} structure differs from known bulk analogs and can be described by a distorted cubic lattice formed in two different directions.
DIAMOND - an Architecture for Persistent Space Platforms
We define DIAMOND, an architecture for generalized, persistent platforms in space, providing support infrastructure for multiple payloads with diverse missions, and able to accept the integration of payloads delivered to the platform after it is established in space. Such platforms would create a new space ecosystem with opportunities for much larger platforms than currently exist, for adaptation to changing technological and market conditions over long periods of time, and for tenants of the platform to launch only their unique payloads without having to carry all the equipment needed to support them. The DIAMOND architecture uses a novel “Architectural Shearing Layer” approach combining long-lived but replaceable structural and support infrastructure components with shorter-lived, higher-value service and tenant facilities. The structural aspect of the proposed architecture is a regular lattice constructed of tetrahedral cells, constructed of only a few types of simple structural components, patterned according to the cubic lattice of natural diamond crystals. The cubic lattice is arranged on larger scales to be fractal sponge, providing a disproportionately large number of surface attachment points while maintaining overall low mass of the entire structure. Generalized architectural shearing layers are also provided that permit easy separation between structural, power, thermal, propulsion/attitude control, pointing/vibration control, computing/data storage, and communication, and various operational aspects of the architecture. The combined result ensures longevity by enabling space platforms to undergo many cycles of change with little peril and at low cost, changing any part of the platform at different times and rates while leaving the remaining parts of the platform undisturbed.
Local and average structures of BaTiO[subscript 3]-Bi(Zn[subscript 1/2]Ti[subscript 1/2])O[subscript 3]
Abstract not provided
Disordered Supersolids in the Extended Bose-Hubbard Model
The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersolid phase tends to be suppressed by disorder. But we also find a narrow parameter window in which the supersolid critical temperature is enhanced by disorder. Our results show that supersolids survive a moderate amount of spatial disorder and thermal fluctuations in the simple cubic lattice.
Publisher Correction: Disordered Supersolids in the Extended Bose-Hubbard Model
The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersolid phase tends to be suppressed by disorder. But we also find a narrow parameter window in which the supersolid critical temperature is enhanced by disorder. Our results show that supersolids survive a moderate amount of spatial disorder and thermal fluctuations in the simple cubic lattice.
Kohn anomalies in momentum dependence of magnetic susceptibility of some three-dimensional systems
We study a question of the presence of Kohn points, yielding at low temperatures nonanalytic momentum dependence of magnetic susceptibility near its maximum, in electronic spectra of some threedimensional systems. In particular, we consider a one-band model on face-centered cubic lattice with hopping between the nearest and next-nearest neighbors, which models some aspects of the dispersion of ZrZn{sub 2}, and the two-band model on body-centered cubic lattice, modeling the dispersion of chromium. For the former model, it is shown that Kohn points yielding maxima of susceptibility exist in a certain (sufficiently wide) region of electronic concentrations; the dependence of the wave vectors, corresponding to the maxima, on the chemical potential is investigated. For the two-band model, we show the existence of the lines of Kohn points, yielding maximum susceptibility, whose position agrees with the results of band structure calculations and experimental data on the wave vector of antiferromagnetism of chromium.
Detailed total scattering analysis of disorder in ZIF-8
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