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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Origin of mean-field behavior in an elastic Ising model

Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. Here, we demonstrate how the long-range interactions responsible for this behavior arise naturally upon integrating out mechanical fluctuations of such a model. A mean-field theory applied to the resulting effective Hamiltonian quantitatively accounts for both thermodynamics and kinetics observed in computer simulations, including a barrier to magnetization reversal that grows extensively with system size. For nanocrystals, which break translational symmetry, a straightforward extension of mean-field theory yields similarly accurate results.

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

Biased degenerate ground-state sampling of small Ising models with converged quantum approximate optimization algorithm

The quantum alternating operator ansatz, a generalization of the quantum approximate optimization algorithm (QAOA), is a quantum algorithm used for approximately solving combinatorial optimization problems. QAOA typically uses the transverse field mixer as the driving Hamiltonian. One of the interesting properties of the transverse field driving Hamiltonian is that it results in nonuniform sampling of degenerate ground states of optimization problems. In this study, we numerically examine the fair sampling properties of the transverse field mixer QAOA, and Grover mixer QAOA (GM-QAOA), which provides theoretical guarantees of fair sampling of degenerate optimal solutions, up to a large enough p such that the mean expectation value converges to an optimal approximation ratio of 1. This comparison is performed with high-quality heuristically computed, but not necessarily optimal, QAOA angles, which give strictly monotonically improving solution quality as p increases. These angles are computed using the Julia based numerical simulation software JuliQAOA. Fair sampling of degenerate ground states is quantified using the Shannon entropy of the ground-state amplitudes distribution. The fair sampling properties are reported on several quantum signature Hamiltonians from previous quantum annealing fair sampling studies. Small random fully connected spin glasses are shown, which exhibit exponential suppression of some degenerate ground states with transverse field mixer QAOA. The transverse field mixer QAOA simulations show that some problem instances clearly saturate the Shannon entropy of 0 with a maximally biased distribution that occurs when the learning converges to an approximation ratio of 1 while other problem instances never deviate from a maximum Shannon entropy (uniform distribution) at any p step. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Ising-CF: A Pathbreaking Collaborative Filtering Method Through Efficient Ising Machine Learning

Due to Ising models’ strong expressivity and Ising machines’ unique computational power, it is highly desired if Ising-based learning can be used in real-world applications. Unfortunately, the challenges in learning Ising models and gaps between the practical accuracy of Ising machines and the theoretical accuracy of Ising models impede the realization of Ising machines’ potential. Hence, we propose an Ising Machine Learning framework, Ising-CF, for collaborative filtering, a widely-used recommendation method. Specifically, Ising-CF uses Linear Neural Networks with Besag’s pseudo-likelihood and voltage polarization for fast, accurate Ising model learning and an Ising-specific logarithmic quantization for ns-level Ising machine inference with near-theoretical accuracy, 7.3% over SOTA.

Liu, Zhuo↗
DOE OSTI2026

Site-decorated model for unconventional frustrated magnets: Ultranarrow phase crossover and two-dimensional spin reversal transition

Here, the site-decorated Ising model is introduced to advance the understanding and experimental realization of the recently discovered one-dimensional (1D) finite-temperature ultranarrow phase crossover in an external magnetic field, while mitigating the geometric complexities of traditional bond-decorated models. The unconventional frustration and physics are clarified by exactly mapping the 1D site-decorated Ising model in a magnetic field onto a zero-field bond-decorated 𝐽 1 −𝐽 2 Ising model with conventional geometrical frustration. Furthermore, although higher-dimensional Ising models in an external field remain unsolved exactly, an exact solution for a spin-reversal transition—driven by an exotic, hidden half-ice, half-fire state induced by site decoration—is derived. This transition, triggered by a slight variation in temperature or magnetic field—without changing its direction—even in the weak-field limit, offers a promising route toward energy-efficient applications such as data storage and processing. The results suggest that site decoration offers an avenue for materials and device design, particularly in systems such as mixed 𝑑−𝑓 compounds, optical lattices, and neural networks, calling for further studies with site-decorated Heisenberg models. In addition, the site-decorated model offers a rigorous test ground for artificial intelligence (AI) in science, as the analytic derivation of the present results was not only validated but also improved by a general-purpose large language model, inspiring the use of AI as scientific discoverer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Ising-Traffic: Using Ising Machine Learning to Predict Traffic Congestion under Uncertainty

This paper addresses the challenges in accurate and realtime traffic congestion prediction with uncertainty by proposing Ising-Traffic, a novel quantum-inspired dual-model Ising based traffic prediction framework which delivers higher accuracy and lower latency than SOTA solutions. While traditional and deep learning methods face the trade-off between algorithm complexity and computational efficiency, our Ising-based method leverages Ising’s inherent and unique capability of finding the state of a system with the lowest energy and applying it to traffic prediction. In this work, traffic prediction under uncertainty is formulated into two separate Ising models: Reconstruct-Ising and Predict-Ising. Reconstruct-Ising is mapped onto modern Ising machine and handles uncertainty in traffic accurately with negligible latency and energy consumption, while Predict-Ising is mapped onto traditional processors and predicts future congestion precisely with only at most 1.8% computational demands of existing solutions. Our evaluation shows Ising-Traffic delivers on average 98× speedups and 5% accuracy improvement over SOTA.

traffic flow control, Ising↗
DOE OSTI2022

Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO 4

We report results of low-temperature heat-capacity, magnetocaloric-effect, and neutron-diffraction measurements of TmVO 4 , an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially filled 4 f orbitals of the thulium (Tm 3 + ) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point by using a magnetic field oriented along the c axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase transition can be well described by using a semiclassical mean-field treatment of the transverse-field Ising model. However, in higher magnetic fields, closer to the field-tuned quantum phase transition, subtle deviations from this semiclassical behavior are observed, which are consistent with expectations of quantum fluctuations. Although the phase transition is driven by the local 4 f degrees of freedom, the crystal lattice still plays a crucial role, both in terms of mediating the interactions between the local quadrupoles and in determining the critical scaling exponents, even though the phase transition itself can be described via mean field. In particular, bilinear coupling of the nematic order parameter to acoustic phonons changes the spatial and temporal fluctuations of the former in a fundamental way, resulting in different critical behavior of the nematic transverse-field Ising model, as compared to the usual case of the magnetic transverse-field Ising model. Our results establish TmVO 4 as a model material and electronic nematicity as a paradigmatic example for quantum criticality in insulators.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Some exactly solvable and tunable frustrated spin models

In this report we discuss three exactly solvable spin models of geometric frustration. First, we discuss a 1-parameter subfamily of the 16 vertex model, which can be mapped to a planar Ising model and solved via Fisher-Dubedát decorations. We then consider a 1-parameter family generalization of the Villain’s fully frustrated model, which interpolates between Onsager’s 2D Ising model and the Villain one. We then discuss spin ice models on a tree, which can be solved exactly using recursions a lá Bethe.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

First-principles calculation of the configurational energy density of states for a solid-state ion conductor with a variant of the Wang and Landau algorithm

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the 1/$\textit{t}$ algorithm, in particular the short iteration performance. Further, a proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor Li 0.5 La 0.5 TiO 3 . This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for Li 0.5 La 0.5 TiO 3 are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the c axis for increasing temperature. In part, the simulation of the disordered Li 0.5 La 0.5 TiO 3 system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Improving Schrödinger Equation Implementations with Gray Code for Adiabatic Quantum Computers

We reformulate the continuous-space Schrödinger equation in terms of spin Hamiltonians. For the kinetic energy operator, the critical concept facilitating the reduction in model complexity is the idea of position encoding. A binary encoding of position produces a spin-1/2 Heisenberg-like model and yields exponential improvement in space complexity when compared to classical computing. Encoding with a binary reflected Gray code (BRGC), and a Hamming-distance-2 Gray code (H2GC) reduces the model complexity down to the 𝑋⁢𝑍 and transverse Ising model, respectively. For 𝐴 qubits BRGC yields 2 𝐴 positions and is reduced to its 2-local form with O⁡(𝐴) ancillary qubits. H2GC yields 2 𝐴/2+1 positions with O⁡(𝐴 2 ) three-local penalty terms. We also identify the bijective mapping between diagonal unitaries and the Walsh series, producing the mapping of any real potential to a series of 𝑘 -local Ising models through the fast Walsh transform. Finally, in a finite volume, we provide some numerical evidence to support the claim that the total time needed for adiabatic evolution is protected by the infrared cutoff of the system. As a result, initial state preparation from a free-field wave function to an interacting system is expected to exhibit polynomial time complexity with volume and constant scaling with respect to lattice discretization for all encodings. For H2GC, if the evolution starts with the transverse Hamiltonian due to hardware restrictions, then penalties are dynamically introduced such that the low-lying spectrum reproduces the energy levels of the Laplacian. The adiabatic evolution of the penalty Hamiltonian is therefore sensitive to the ultraviolet scale. It is expected to exhibit polynomial time complexity with lattice discretization, or exponential time complexity with respect to the number of qubits given a fixed volume.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On the origin of cooperativity effects in the formation of self-assembled molecular networks at the liquid/solid interface

In this work we investigate the behaviour of molecules at the nanoscale using scanning tunnelling microscopy in order to explore the origin of the cooperativity in the formation of self-assembled molecular networks (SAMNs) at the liquid/solid interface. By studying concentration dependence of alkoxylated dimethylbenzene, a molecular analogue to 5-alkoxylated isophthalic derivatives, but without hydrogen bonding moieties, we show that the cooperativity effect can be experimentally evaluated even for low-interacting systems and that the cooperativity in SAMN formation is its fundamental trait. We conclude that cooperativity must be a local effect and use the nearest-neighbor Ising model to reproduce the coverage vs. concentration curves. The Ising model offers a direct link between statistical thermodynamics and experimental parameters, making it a valuable tool for assessing the thermodynamics of SAMN formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗