Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Ising Model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Observation of Unprecedented Fractional Magnetization Plateaus in a New Shastry-Sutherland Ising Compound

Geometrically frustrated magnetic systems, such as those based on the Shastry-Sutherland lattice (SSL), offer a rich playground for exploring unconventional magnetic states. The delicate balance between competing interactions in these systems leads to the emergence of novel phases. We present the characterization of Er 2 ⁢Be 2⁢ GeO 7 , an SSL compound with Er 3+ ions forming orthogonal dimers separated by nonmagnetic layers whose structure is invariant under the 𝑃⁢$\bar{4}21$⁢𝑚 space group. Neutron scattering reveals an antiferromagnetic dimer structure at zero field, typical of Ising spins on that lattice and consistent with the anisotropic magnetization observed. However, magnetization measurements exhibit fractional plateaus at 1/4 and 1/2 of saturation, in contrast to the expected 1/3 plateau of the SSL Ising model. By comparing the energy of candidate states with ground-state lower bounds we show that this behavior requires spatially anisotropic interactions, leading to an anisotropic Shastry-Sutherland Ising model symmetric under the 𝐶⁢𝑚⁢𝑚⁢2 space group. This anisotropy is consistent with the small orthorhombic distortion observed with single-crystal neutron diffraction. The other properties, including thermodynamics, which have been investigated theoretically using tensor networks, point to small residual interactions, potentially due to further couplings and quantum fluctuations. This study highlights Er 2 ⁢Be 2 ⁢GeO 7 as a promising platform for investigating exotic magnetic phenomena.

Yadav, Lalit [Duke University, Durham, NC (United ↗
DOE OSTI2023

Simulating Quantum Systems with NWQ-Sim on HPC

NWQ-Sim is a cutting-edge quantum system simulation environment designed to run on classical multi-node, multi-CPU/GPU heterogeneous HPC systems. In this work, we provide a brief overview of NWQ-Sim and its implementation in simulating quantum circuit applications, such as the transverse field Ising model. We also demonstrate how NWQ-Sim can be used to examine the effects of errors that occur on real quantum devices, using a combined device noise model. Moreover, NWQ-Sim is particularly well-suited for implementing variational quantum algorithms where circuits are dynamically generated. Therefore, we also illustrate this with the variational quantum eigensolver (VQE) for the Ising model. In both cases, NWQ-Sim's performance is comparable to or better than alternative simulators. We conclude that NWQ-Sim is a useful and flexible tool for simulating quantum circuits and algorithms, with performance advantages and noise-aware simulation capabilities.

Suh, In-Saeng↗
DOE OSTI2025

Real-Time Operator Evolution in Two and Three Dimensions via Sparse Pauli Dynamics

We study real-time operator evolution using sparse Pauli dynamics, a recently developed method for simulating expectation values of quantum circuits. On the examples of energy and charge diffusion in one-dimensional (1D) spin chains and sudden quench dynamics in the 2D transverse-field Ising model, it is shown that this approach can compete with state-of-the-art tensor network methods. We further demonstrate the flexibility of the approach by studying quench dynamics in the 3D transverse-field Ising model that is highly challenging for tensor network methods. For the simulation of expectation value dynamics starting in a computational basis state, we introduce an extension of sparse Pauli dynamics that truncates the growing sum of Pauli operators by discarding terms with a large number of X and Y matrices. This is validated by our 2D and 3D simulations. Finally, we argue that sparse Pauli dynamics is not only capable of converging challenging observables to high accuracy, but can also serve as a reliable approximate approach even when given only limited computational resources. Published by the American Physical Society 2025

Begušić, Tomislav (ORCID:0000000279424134)↗
DOE OSTI2025

Ising on $\mathbb{S}^2$-- The Affine Conjecture

We review the recent construction \cite{brower2024isingmodelmathbbs2} of the 2d Ising model on a triangulated sphere $\mathbb{S}^2$. Surprisingly, this led to a precise map of the lattice couplings to the target geometry in order to reach the conform field theory (CFT) in the continuum limit. For the integrable 2d Ising CFT, the map was found analytically \cite{Brower_2023}. Here we conjecture how this might be generalized. The discrete geometry is implemented by the piecewise flat triangulation introduced by Regge in 1960 for the Einstein Hilbert action \cite{Regge1961GeneralRW}. Then following our Ising example, we posit the existence of a smooth map of lattice couplings in affine parameters consistent with quantum correlators. A sequence of theoretical investigations and numerical simulations are recommended to test this conjecture. They begin with non-integrable CFT's -- the 2d $\phi^4$ theory on $\mathbb{S}^2$; the 3d Ising model on $\mathbb{S}^3$ and $\mathbb{R} \times \mathbb{S}^2$; QED3 on $\mathbb{R} \times \mathbb{S}^{2} $ as an intermediate step to 4d non-Abelian lattice gauge theory on $\mathbb{R} \times \mathbb{S}^3$.

Brower, Richard C. [Boston U.] (ORCID:000000028185↗
DOE OSTI2025

Interactions Enhance Ramp Reversal Memory in Locally Phase Separated Materials

The ramp-reversal memory (RRM) effect in metal–insulator transition metal oxides (TMOs), a non-volatile resistance change induced by repeated temperature cycling, has attracted considerable interest in neuromorphic computing and non-volatile memory devices. Our previous defect motion model successfully explained RRM in vanadium dioxide (VO 2 ), capturing observed critical temperature shifts and memory accumulation throughout the sample. However, this approach lacked interactions between metallic and insulating domains. Here, we extend our model by combining a correlated Random Field Ising Model with defect diffusion-segregation, enabling accurate hysteresis modeling while predicting the relationship between RRM and domain interactions. Our simulations demonstrate that the maximum RRM occurs when the turnaround temperature approaches the inflection point. This peak in RRM vs. turnaround temperature is consistent with prior transport measurements, as well as our own optical measurements reported here. Significantly, we find that increasing nearest-neighbor interactions enhances the maximum memory effect, thus providing a clear mechanism for optimizing RRM performance. Since our model employs minimal assumptions, we predict that RRM should be a widespread phenomenon in materials exhibiting patterned phase coexistence of electronic domains. This work not only advances fundamental understanding of memory behavior in TMOs but also establishes a much-needed theoretical framework for optimizing device applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs

Abstract We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Probing criticality with deep learning in relativistic heavy-ion collisions

Systems with different interactions could develop the same critical behavior due to the underlying symmetry and universality. Using this principle of universality, we can embed critical correlations modeled on the 3D Ising model into the simulated data of heavy-ion collisions, hiding weak signals of a few inter-particle correlations within a large particle cloud. Employing a point cloud network with dynamical edge convolution, we are able to identify events with critical fluctuations through supervised learning, and pick out a large fraction of signal particles used for decision-making in each single event.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Trotter Errors from Dynamical Structural Instabilities of Floquet Maps in Quantum Simulation

We study the behavior of errors in the quantum simulation of spin systems with long-range multibody interactions resulting from the Trotter-Suzuki decomposition of the time-evolution operator. We identify a regime where the Floquet operator underlying the Trotter decomposition undergoes sharp changes even for small variations in the simulation step size. This results in a time evolution operator that is very different from the dynamics generated by the targeted Hamiltonian, which leads to a proliferation of errors in the quantum simulation. These regions of sharp change in the Floquet operator, referred to as structural instability regions, appear typically at intermediate Trotter step sizes and in the weakly interacting regime, and are thus complementary to recently revealed quantum chaotic regimes of the Trotterized evolution [L. M. Sieberer et al. npj Quantum Inf. 5, 78 (2019); M. Heyl, P. Hauke, and P. Zoller, Sci. Adv. 5, eaau8342 (2019)]. We characterize these structural instability regimes in p-spin models, transverse-field Ising models with all-to-all p-body interactions, and analytically predict their occurrence based on unitary perturbation theory. We further show that the effective Hamiltonian associated with the Trotter decomposition of the unitary time-evolution operator, when the Trotter step size is chosen to be in the structural instability region, is very different from the target Hamiltonian, which explains the large errors that can occur in the simulation in the regions of instability. These results have implications for the reliability of near-term gate-based quantum simulators, and reveal an important interplay between errors and the physical properties of the system being simulated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Renormalization of Ising cage-net model and generalized foliation

A large class of type-I fracton models, including the X-cube model, have been found to be fixed points of the foliated renormalization group (RG). The system size of such foliated models can be changed by adding or removing decoupled layers of 2D topological states and continuous deformation of the Hamiltonian. In this paper, we study a closely related model—the Ising cage-net model—and find that this model is not foliated in the same sense. In fact, we point out certain unnatural restrictions in the foliated RG, and find that removing these restrictions leads to a generalized foliated RG under which the Ising cage-net model is a fixed point, and which includes the original foliated RG as a special case. The Ising cage-net model thus gives a prototypical example of the generalized foliated RG, and its system size can be changed either by condensing/uncondensing bosonic planon excitations near a 2D plane or through a linear-depth quantum circuit in the same plane. Additionally, we show that these two apparently different RG procedures are closely related, as they lead to the same gapped boundary when implemented in part of a plane. Finally, we briefly discuss the implications for foliated fracton phases, whose universal properties will need to be reexamined in light of the generalized foliated RG.

2-dimensional systems↗
DOE OSTI2022

Random strain induced correlations in materials with intertwined nematic and magnetic orders

Electronic nematicity is rarely observed as an isolated instability of a correlated electron system. Instead, in iron pnictides and in certain cuprates and heavy-fermion materials, nematicity is intertwined with an underlying spin-stripe or charge-stripe state. As a result, random strain, ubiquitous in any real crystal, creates both random-field disorder for the nematic degrees of freedom and random-bond disorder for the spin or charge ones. Here, we put forward an Ashkin-Teller model with random Baxter fields to capture the dual role of random strain in nematic systems for which nematicity is a composite order arising from a stripe state. Using Monte Carlo to simulate this random Baxter-field model, we find not only the expected break-up of the system into nematic domains, but also the emergence of nontrivial disorder-promoted magnetic correlations. Such correlations enhance and tie up the fluctuations associated with the two degenerate magnetic stripe states from which nematicity arises, leaving characteristic signatures in the spatial profile of the magnetic domains, in the configurational space of the spin variables, and in the magnetic noise spectrum. We discuss possible experimental manifestations of these effects in iron-pnictide superconductors. Furthermore, our work establishes the random Baxter-field model as a more complete alternative to the random-field Ising model to describe complex electronic nematic phenomena in the presence of disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Quantum Mpemba effect without global symmetries

The Mpemba effect, where a system initially farther from equilibrium relaxes faster than one closer to equilibrium, has been extensively studied in classical systems and recently explored in quantum settings. While previous studies of the quantum Mpemba effect (QME) have largely focused on isolated systems with global symmetries, we argue that the QME is ubiquitous in generic, nonintegrable many-body systems lacking such symmetries, including U(1) charge conservation, spatial symmetries, and even energy conservation. Using paradigmatic models such as the quantum Ising model with transverse and longitudinal fields, we show that the QME can be understood through the energy density of initial states and their inverse participation ratio in the energy eigenbasis. Our findings provide a unified framework for the QME, linking it with classical thermal relaxation.

Bhore, Tanmay [University of Leeds (United Kingdom↗
DOE OSTI2021

Clock model interpolation and symmetry breaking in O(2) models

The $q$-state clock model is a classical spin model that corresponds to the Ising model when $q=2$ and to the $XY$ model when $q\to\infty$. The integer-$q$ clock model has been studied extensively and has been shown to have a single phase transition when $q=2$,$3$,$4$ and two phase transitions when $q>4$.We define an extended $q$-state clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuous interpolation of the clock model to noninteger $q$. We investigate this class of clock models in 2D using Monte Carlo (MC) and tensor renormalization group (TRG) methods, and we find that the model with noninteger $q$ has a crossover and a second-order phase transition. We also define an extended-$O(2)$ model (with a parameter $\gamma$) that reduces to the $XY$ model when $\gamma=0$ and to the extended $q$-state clock model when $\gamma\to\infty$, and we begin to outline the phase diagram of this model. These models with noninteger $q$ serve as a testbed to study symmetry breaking in situations corresponding to quantum simulators where experimental parameters can be tuned continuously.

Hostetler, Leon↗
NASA NTRS1985

A remark about pointed bubbles

The polymer expansion is a formal algebraic identity between a partition function and logarithm in statistical physics problems. The expansion gives a systematic method to control the free energy or to establish exponential tree-graph decay of connected correlations. Here, the convergence properties of the polymer expansion are analyzed in connection with three practical examples, including: intersecting bonds in chemical polymer chains; a connected closed hypersurface built from the (d-1)-faces of the d-dimensional unit cubes; and the set of Feynamn diagrams in the perturbation series of the Euclidean field theory partition function Z. The example of connected polymer chains is generalized to apply to other lattice models, including n-state Ising models at high temperature; short range lattice gases at high temperature; and weak coupling lattice field and gauge theories.

Garabedian, P. R.↗
DOE OSTI2021

Bayesian Learning of Adatom Interactions from Atomically Resolved Imaging Data

Atomic structures and adatom geometries of surfaces encode information about the thermodynamics and kinetics of the processes that lead to their formation, and which can be captured by a generative physical model. In this work, we develop a workflow based on a machine-learning-based analysis of scanning tunneling microscopy images to reconstruct the atomic and adatom positions, and a Bayesian optimization procedure to minimize statistical distance between the chosen physical models and experimental observations. We optimize the parameters of a 2- and 3-parameter Ising model describing surface ordering and use the derived generative model to make predictions across the parameter space. For concentration dependence, we compare the predicted morphologies at different adatom concentrations with the dissimilar regions on the sample surfaces that serendipitously had different adatom concentrations. The proposed workflow can be used to reconstruct the thermodynamic models and associated uncertainties from the experimental observations of materials microstructures. The code used in the manuscript is available at https://github.com/saimani5/Adatom_interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Half-ice, half-fire-driven ultranarrow phase crossover in one-dimensional decorated 𝑞-state Potts ferrimagnets: An AI-co-led exploration

OpenAI’s reasoning model o3-mini-high was used to carry out an exact analytic study of one-dimensional ferrimagnetic site- and bond-decorated 𝑞-state Potts models. We demonstrate that the finite-temperature ultranarrow phase crossover (UNPC), driven by a hidden “half-ice, half-fire” state recently discovered in the 𝑞=2 case (Ising model), persists for 𝑞>2. Moreover, we identify unique features for 𝑞>2, including the dome structure in the field-temperature phase diagram, and for large 𝑞 a secondary high-temperature UNPC to the fully disordered paramagnetic state. As the UNPC quickly approaches a genuine transition by enhancing 𝐽, the interaction between the backbone spins, two distinct behaviors emerge: In the site-decorated Potts model, 𝑇 0 is independent of 𝐽 and thus remains unchanged (Type-I UNPC), and in the bond-decorated Potts model with 𝑞>2, 𝑇 0 depends on 𝐽 and quickly shifts toward a finite temperature as 𝐽 increases (Type-II UNPC). These results establish a versatile framework for engineering controlled fast state-flipping switches in low-dimensional systems. Our nine-dan artificial intelligence (AI)-contribution framework assigns AI the meritorious status of AI-co-led discovery in this work.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Infinite neural network quantum states: entanglement and training dynamics

We study infinite limits of neural network quantum states (∞-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of entanglement entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. The analytic calculations of entanglement entropy bound are tractable because the ensemble statistics are simplified in the Gaussian process limit. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For ∞-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an ∞-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. ∞-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.

quantum state supervised learning↗
DOE OSTI2020

Confinement, reduced entanglement, and spin-glass order in a random quantum spin-ice model

In this work, we study an effective spin model derived perturbatively from a random transverse-field Ising model on the pyrochlore lattice. The model consists of spin configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization up to N=64 site systems. Furthermore, we calculate spin-glass correlation functions and local entanglement entropy S T between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where S T =ln 6. Increasing randomness, at low transverse fields, first leads to a frozen phase, with long-range spin-glass order and S T =ln 2 corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Size- and temperature-dependent magnetization of iron nanoclusters

In this paper, the magnetic behavior of bcc iron nanoclusters, with diameters between 2 and 8 nm, is investigated by means of spin dynamics simulations coupled to molecular dynamics, using a distance-dependent exchange interaction. Finite-size effects in the total magnetization as well as the influence of the free surface and the surface/core proportion of the nanoclusters are analyzed in detail for a wide temperature range, going beyond the cluster and bulk Curie temperatures. Comparison is made with experimental data and with theoretical models based on the mean-field Ising model adapted to small clusters, and taking into account the influence of low coordinated spins at free surfaces. Our results for the temperature dependence of the average magnetization per atom M (T), including the thermalization of the transnational lattice degrees of freedom, are in very good agreement with available experimental measurements on small Fe nanoclusters. In contrast, significant discrepancies with experiment are observed if the translational degrees of freedom are artificially frozen. The finite-size effects on M (T) are found to be particularly important near the cluster Curie temperature. Simulated magnetization above the Curie temperature scales with cluster size as predicted by models assuming short-range magnetic ordering. Analytical approximations to the magnetization as a function of temperature and size are proposed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗