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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Magnetic Properties of Simplest Pure Husimi Lattice: a Monte Carlo Study

The magnetic properties of a Husimi lattice with antiferromagnetic spins-|S| = 1/2, 1, 3/2, and 2 Ising model with three sites in the elementary polygon (p = 3) and the coordination number z = 4 have been investigated using a Monte Carlo study. The reduced critical temperature is deduced for different values of magnetic external field, for a fixed value of crystal field and spin moments. The magnetization versus the crystal field is determined for different values of temperatures and for different values of external magnetic field and spin moments. The hysteresis curves of magnetization with the magnetic field have been established for different values of reduced temperatures, reduced crystal field, and spin moments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

One-Sided Continuity Properties for the Schonmann Projection

We consider the plus-phase of the two-dimensional Ising model below the critical temperature. In 1989 Schonmann proved that the projection of this measure onto a one-dimensional line is not a Gibbs measure. After many years of continued research which have revealed further properties of this measure, the question whether or not it is a Gibbs measure in an almost sure sense remains open. In this paper we study the same measure by interpreting it as a temporal process. One of our main results is that the Schonmann projection is almost surely a regular g-measure. That is, it does possess the corresponding one-sided notion of almost Gibbsianness. We further deduce strong one-sided mixing properties which are of independent interest. Our proofs make use of classical coupling techniques and some monotonicity properties which are known to hold for one-sided, but not two-sided conditioning for FKG measures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Moment method and continued fraction expansion in Floquet operator Krylov space

Recursion methods such as Krylov techniques map complex dynamics to an effective noninteracting problem in one dimension. For example, the operator Krylov space for Floquet dynamics can be mapped to the dynamics of an edge operator of the one-dimensional Floquet inhomogeneous transverse field Ising model (ITFIM), where the latter, after a Jordan-Wigner transformation, is a Floquet model of noninteracting Majorana fermions and the couplings correspond to Krylov angles. We present an application of this showing that a moment method exists where given an autocorrelation function, one can construct the corresponding Krylov angles and from that the corresponding Floquet ITFIM. Consequently, when no solutions for the Krylov angles are obtained, it indicates that the autocorrelation is not generated by unitary dynamics. We highlight this by studying certain special cases: stable m-period dynamics derived using the method of continued fractions, exponentially decaying, and power-law decaying stroboscopic dynamics. Remarkably, our examples of stable m-period dynamics correspond to m-period edge modes for the Floquet ITFIM where, deep in the chain, the couplings correspond to a critical phase. Furthermore our results pave the way to engineer Floquet systems with desired properties of edge modes and also provide examples of persistent edge modes in gapless Floquet systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

A theoretical calculation of stacking fault energy of Ni alloys: The effects of temperature and composition

Combining cluster expansion (CE) method with one dimensional axial Ising model, this work investigated the effects of alloying elements and configurational variations due to temperature on the stacking fault energy (SFE) of FCC Ni binary alloys. Ensembles of large numbers of atomistic structures, each with more than ~400 atoms, were generated to consider sufficient long-range chemical disorder and temperature effects due to configurational entropy. Here, a Monte Carlo Metropolis algorithm was used to generate these structures, whose energies were then evaluated based on the effective cluster interactions obtained from CE. As a baseline, this work had shown the SFE of pure Ni and Al to be 127 mJ/m 2 and 137 mJ/m 2 , respectively, which agreed with the experimental values of 125 mJ/m 2 and 150 mJ/m 2 reported in the literature. Additions of Al, Ti, Cr and Co to pure Ni were found to decrease the SFE to different extents. Although temperature does not strongly influence the SFE of the FCC Ni-Al and Ni-Cr binary alloys, it can lead to significant changes to the SFE of the FCC Ni-Ti and Ni-Co alloys. While effects of temperature and composition on SFE observed in this work were calculated from binary Ni alloys, the general trends are nonetheless expected to be valid in the γ phase of multicomponent Ni superalloys.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Domain wall kinetics of lithium niobate single crystals near the hexagonal corner

A mesospheric approach based on a simple microscopic 2D Ising model in a hexagonal lattice plane is proposed to explain macroscopic “asymmetric in-out domain wall motion” observation in the (0001) plane of MgO-doped stoichiometric lithium niobate. Under application of an electric field that was higher than the conventional coercive field (E{sub c}) to the ferroelectric crystal, a natural hexagonal domain was obtained with walls that were parallel to the Y-axis of the crystal. When a fraction of the coercive field of around 0.1E{sub c} is applied in the reverse direction, this hexagonal domain is shrunk (moved inward) from the corner site into a shape with a corner angle of around 150° and 15° wall slopes to the Y-axis. A flipped electric field of 0.15E{sub c} is then applied to recover the natural hexagonal shape, and the 150° corner shape changes into a flat wall with 30° slope (moved outward). The differences in corner domain shapes between inward and outward domain motion were analyzed theoretically in terms of corner and wall site energies, which are described using the domain corner angle and wall slope with respect to the crystal Y-axis, respectively. In the inward domain wall motion case, the energy levels of the evolving 150° domain corner and 15° slope walls are most competitive, and could co-exist. In the outward case, the energy levels of corners with angles >180° are highly stable when compared with the possible domain walls; only a flat wall with 30° slope to the Y-axis is possible during outward motion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Scaling study of magnetic phase transition and critical behavior in Nd0.55Sr0.45Mn0.98Ga0.02O3 manganite

Highlights: • The sample of Nd{sub 0.55}Sr{sub 0.45}Mn{sub 0.98}Ga{sub 0.02}O{sub 3} was synthesized via a solid state reaction route. • The PM to FM phase transition of this sample is found to be of second-order. • The critical behaviors and scaling relation for Nd{sub 0.55}Sr{sub 0.45}Mn{sub 0.98}Ga{sub 0.02}O{sub 3} have also been investigated by modified Arrott plot and critical isotherm analysis. • The estimated critical exponents are close to the values for 3D-Ising model. - Abstract: Microscopic magnetic interactions and magnetism can be probed by studying the critical paramagnetic–ferromagnetic phase transition of magnetic materials. In this work, the critical behavior of the lightly Ga-doped manganites Nd{sub 0.55}Sr{sub 0.45}Mn{sub 0.98}Ga{sub 0.02}O{sub 3} (NSMGO) has been investigated. Scaling analysis reveals the critical exponents β = 0.308, γ = 1.197, and δ = 4.916, where their self-consistency and reliability are verified by the Widom scaling law and the scaling equation. These exponents indicate that the magnetic phase transition in NSMGO belongs to the anisotropic 3D-Ising universality class. Nevertheless, the asymptotic critical exponents β{sub eff} and γ{sub eff} are found to approach to the values of 3D-Heisenberg model, implying the existence of isotropic short-range magnetic interactions. We suggest that, although the Nd-based manganites possess a strong magnetocrystalline anisotropy, this effect can be partly averaged out in view of the present polycrystalline NSMGO. Therefore, in the asymptotic critical region, the phase transition reveals the crossover from the scaling of 3D-Ising toward 3D-Heisenberg universality class.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Equilibrium, metastability, and hysteresis in a model spin-crossover material with nearest-neighbor antiferromagnetic-like and long-range ferromagnetic-like interactions

Phase diagrams and hysteresis loops were obtained by Monte Carlo simulations and a mean- field method for a simplified model of a spin-crossovermaterialwith a two-step transition between the high-spin and low-spin states. This model is a mapping onto a square-lattice S = 1/2 Ising model with antiferromagnetic nearest-neighbor and ferromagnetic Husimi-Temperley ( equivalent-neighbor) long-range interactions. Phase diagrams obtained by the two methods for weak and strong long-range interactions are found to be similar. However, for intermediate-strength long-range interactions, the Monte Carlo simulations show that tricritical points decompose into pairs of critical end points and mean-field critical points surrounded by horn-shaped regions of metastability. Hysteresis loops along paths traversing the horn regions are strongly reminiscent of thermal two-step transition loops with hysteresis, recently observed experimentally in several spin-crossover materials. As a result, we believe analogous phenomena should be observable in experiments and simulations for many systems that exhibit competition between local antiferromagnetic-like interactions and long-range ferromagnetic-like interactions caused by elastic distortions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Operator product expansion for radial lattice quantization of 3D ϕ 4 theory

At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3D Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the quantum finite elements method to implement radially quantized critical ϕ 4 theory on simplicial lattices approaching R × S 2 . Computing the four-point function of identical scalars, we demonstrate the power of radial quantization by the accurate determination of the scaling dimensions Δ ε and Δ T as well as ratios of the operator product expansion coefficients f σ σ ε and f σ σ T of the first spin-0 and spin-2 primary operators ε and T of the 3D Ising CFT. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

An Ising Spin-2 Model on Generalized Recursive Lattice: a Monte Carlo Study

The magnetic properties of Ising spin-2 model on recursive p-polygonal structures are studied using Monte Carlo simulations. The thermal magnetization and magnetic susceptibility of recursive 1-, 2-, 3-, and 4-polygonal structures have been terminated. The variation of magnetization and magnetic susceptibility of recursive 2-polygonal structures for several external magnetic field and the variation of magnetization and magnetic susceptibility versus the crystal field and temperatures of recursive 1-, 2-, 3-, and 4-polygonal structures are given. Finally, the magnetic hysteresis cycle of recursive 1-, 2-, 3-, and 4-polygonal structures are obtained and for different temperatures with 2-polygonal structures. It is shown that the reduced transition temperature increases with increasing the p-polygonal structures and decreases with increasing the absolute value of crystal field. The magnetic coercive field increases with increasing the p-polygonal structures and decreases with increasing the temperature values. The superparamagnetism behavior is observed in our system at around reduced transition temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1992

Random-anisotropy Blume-Emery-Griffiths model

The results are described of studies of a random-anisotropy Blume-Emery-Griffiths spin-1 Ising model using mean-field theory, transfer-matrix calculations, and position-space renormalization-group calculations. The interplay between the quenched randomness of the anisotropy and the annealed disorder introduced by the spin-1 model leads to a rich phase diagram with a variety of phase transitions and reentrant behavior. The results may be relevant to the study of the phase separation of He-3 - He-4 mixtures in porous media in the vicinity of the superfluid transition.

Maritan, Amos↗
DOE OSTI2022

Algebraic compression of quantum circuits for Hamiltonian evolution

Here unitary evolution under a time-dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits the depth of which scales with the number of steps. When the circuit elements are limited to a subset of SU(4) - or equivalently, when the Hamiltonian may be mapped onto free fermionic models - several identities exist that combine and simplify the circuit. Based on this, we present an algorithm that compresses the Trotter steps into a single block of quantum gates using algebraic relations between adjacent circuit elements. This results in a fixed depth time evolution for certain classes of Hamiltonians. We explicitly show how this algorithm works for several spin models, and demonstrate its use for adiabatic state preparation of the transverse field Ising model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Complete catalog of ground-state diagrams for the general three-state lattice-gas model with nearest-neighbor interactions on a square lattice

Here, the ground states of the general three-state lattice-gas (equivalently, S = 1 Ising) model with nearest-neighbor interactions on a square lattice are explored in the full, five-dimensional parameter space of three interaction constants and two generalized chemical potentials or fields. The complete catalog of fifteen topologically different ground-state diagrams (zero-temperature phase diagrams), which show the regions of stability of the different ground states in the full parameter space of the model, is obtained and discussed in both lattice-gas and Ising-spin language. The results extend those of a recent study in a reduced parameter space, which identified six topologically different ground-state diagrams.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Inferring the Isotropic-Nematic Phase Transition with Generative Machine Learning

Generative machine learning models are capable of learning the phase behavior in condensed matter systems such as the Ising model. We utilize a score-based modeling procedure called thermodynamic maps to describe the isotropic-nematic phase transition in a melt of Gay-Berne ellipsoids. When trained on samples from a single temperature on either side of the phase transition, this generative machine learning approach infers effectively the nematic order parameter at intermediate temperatures. Furthermore, these results demonstrate score-based models’ ability to learn the physics of a nontrivial liquid crystal phase transition.

Critical exponents↗
DOE OSTI2025

Discrete generative diffusion models without stochastic differential equations: A tensor network approach

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025

Causer, Luke (ORCID:0000000194243473)↗
DOE OSTI2018

Learning local, quenched disorder in plasticity and other crackling noise phenomena

Abstract When far from equilibrium, many-body systems display behavior that strongly depends on the initial conditions. A characteristic such example is the phenomenon of plasticity of crystalline and amorphous materials that strongly depends on the material history. In plasticity modeling, the history is captured by a quenched, local and disordered flow stress distribution. While it is this disorder that causes avalanches that are commonly observed during nanoscale plastic deformation, the functional form and scaling properties have remained elusive. In this paper, a generic formalism is developed for deriving local disorder distributions from field-response (e.g., stress/strain) timeseries in models of crackling noise. We demonstrate the efficiency of the method in the hysteretic random-field Ising model and also, models of elastic interface depinning that have been used to model crystalline and amorphous plasticity. We show that the capacity to resolve the quenched disorder distribution improves with the temporal resolution and number of samples.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Onset of Scrambling as a Dynamical Transition in Tunable-Range Quantum Circuits

In a fast-scrambling many-body quantum system, information is spread and entanglement is built up on a time scale that grows logarithmically with the system size. This is of fundamental interest in understanding the dynamics of many-body systems, as well as in efficiently producing entangled resource states and error-correcting codes. In this work, we identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity. In particular, we show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse around a critical point between two clearly defined regimes of different dynamical behavior. We study this transition analytically in a related long-range Brownian-circuit model and show how the transition can be mapped onto the statistical mechanics of a long-range Ising model in a particular region of parameter space. This mapping predicts mean-field critical exponents v=–1/(1 + s c ), which are consistent with the critical exponents extracted from Clifford-circuit numerics. In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic sparse circuits that can be realized in experiments with neutral-atom arrays.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Universal model of Floquet operator Krylov space

It is shown that the stroboscopic time evolution under a Floquet unitary, in any spatial dimension, and of any Hermitian operator, can be mapped to an operator Krylov space, which is identical to that generated by the edge operator of the noninteracting Floquet transverse-field Ising model (TFIM) in one-spatial dimension, and with inhomogeneous Ising and transverse field couplings. The latter has four topological phases reflected by the absence (topologically trivial) or presence (topologically nontrivial) of edge modes at 0 and/or π quasienergies. It is shown that the Floquet dynamics share certain universal features characterized by how the Krylov parameters vary in the topological phase diagram of the Floquet TFIM with homogeneous couplings. Furthermore, these results are highlighted through examples, all chosen for numerical convenience to be in one spatial dimension: nonintegrable Floquet spin 1/2 chains and Floquet Z 3 clock model where the latter hosts period-tripled edge modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Quantum phase transitions in long-range interacting hyperuniform spin chains in a transverse field

Hyperuniform states of matter are characterized by anomalous suppression of long-wavelength density fluctuations. While most of the interesting cases of disordered hyperuniformity are provided by complex many-body systems such as liquids or amorphous solids, classical spin chains with certain long-range interactions have been shown to demonstrate the same phenomenon. Such spin-chain systems are ideal models for exploring the effects of quantum mechanics on hyperuniformity. It is well-known that the transverse field Ising model shows a quantum phase transition (QPT) at zero temperature. Under the quantum effects of a transverse magnetic field, classical hyperuniform spin chains are expected to lose their hyperuniformity. High-precision simulations of these cases are complicated because of the presence of highly nontrivial long-range interactions. We perform an extensive analysis of these systems using density matrix renormalization group simulations to study the possibilities of phase transitions and the mechanism by which they lose hyperuniformity. Even for a spin chain of length 30, we see discontinuous changes in properties like the “τ order metric” of the ground state, the measure of hyperuniformity, and the second cumulant of the total magnetization along the x-direction, all suggestive of first-order QPTs. An interesting feature of the phase transitions in these disordered hyperuniform spin chains is that, depending on the parameter values, the presence of a transverse magnetic field may lead remarkably to an increase in the order of the ground state as measured by the “τ order metric,” even if hyperuniformity is lost. Therefore, it would be possible to design materials to target specific novel quantum behaviors in the presence of a transverse magnetic field. Our numerical investigations suggest that these spin chains can show no more than two QPTs. We further analyze the long-range interacting spin chains via the Jordan-Wigner mapping onto a system of spinless fermions, showing that under the pairwise-interaction approximation and a mean-field treatment, there can be at most two quantum phase transitions. Here, based on these numerical and theoretical explorations, we conjecture that for spin chains with long-range pair interactions that have convergent cosine transforms, there can be a maximum of two quantum phase transitions at zero temperature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗