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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Kibble–Zurek mechanism of Ising domains

The formation of topological defects after a symmetry-breaking phase transition is an overarching phenomenon that encodes the underlying dynamics. The Kibble-Zurek mechanism (KZM) describes these non-equilibrium dynamics of second-order phase transitions and predicts a power-law relationship between the cooling rates and the density of topological defects. It has been verified as a successful model in a wide variety of physical systems, including structure formation in the early Universe and condensed-matter materials. However, it is uncertain if the KZM mechanism is also valid for topologically trivial Ising domains, one of the most common and fundamental types of domain in condensed-matter systems. Here we show that the cooling rate dependence of Ising domain density follows the KZM power law in two different three-dimensional structural Ising domains: ferro-rotation domains in NiTiO 3 and polar domains in BiTeI. However, although the KZM slope of NiTiO 3 agrees with the prediction of the 3D Ising model, the KZM slope of BiTeI exceeds the theoretical limit, providing an example of steepening KZM slope with long-range dipolar interactions. Finally, our results demonstrate the validity of KZM for Ising domains and reveal an enhancement of the power-law exponent for transitions of non-topological quantities with long-range interactions. The Kibble-Zurek mechanism is shown to apply to structural Ising domains in three-dimensional materials. Long-range interactions modify the critical exponents away from theoretical predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1982

Data from ISEE-3 for the IMS period

The International Sun-Earth Explorer (ISEE) Project represents a joint effort between the European Space Agency and NASA. The primary objective of the project is the study of the outer magnetosphere. A review is presented concerning the data available from ISEE-3 up to the end of the International Magnetospheric Study (IMS) period (December 31, 1979), taking into account the approaches used to obtain the data. Attention is given to the ISEE-3 as an upstream monitor, ISEE-3 an an observer of the magnetosphere, aspects of ISEE-3 data availability, questions regarding the data link, and the definitive orbit position of ISEE-3 throughout the IMS.

Von Rosenvinge, T. T.↗
NASA NTRS1987

Simultaneous measurements of the magnetopause and flux transfer events at widely separated sites by AMPTE UKS and ISEE 1 and 2

On September 19, 1984, the ISEE 1 and 2 and AMPTE UKS and IRM spacecraft pairs crossed the dayside magnetopause at nearly the same universal time and magnetic local time but at much different latitudes. This fortuitous ocurrence allows the magnetopause and flux transfer events (FTEs) to be studied at two widely separated sites simultaneously. FTEs are observed at both locations, those at UKS having standard normal component signatures, while those at ISEE have reverse signatures. The FTEs at UKS, closer to the equator, appear to have less helicity, or 'twistedness' than those at ISEE far to the south. By identifying FTEs using the stringent Rijnbeek et al. (1984) criterion for the bipolar B(n) signature it might be concluded that FTEs are not necessarily detected simultaneously at UKS and ISEE. However, careful analysis of the field strength behavior at ISEE does reveal evidence that FTEs are indeed observed at both sites simultaneously. While within the magnetosphere, AMPTE and ISEE both observe a coherent field rarefaction coupled with a tilt; it is speculated that the signature is associated with time-dependent dayside magnetopause reconnection.

Elphic, R. C.↗
NASA NTRS1992

ISEE 3 plasmoid and TCR observations during an extended interval of substorm activity

On April 9-11, 1983, the ISEE 3 spacecraft was continuously located within the earth's magnetotail for more than 36 hours at downstream distances of X = -76 to -80 R(e). During this span of time, 12 major intervals of substorm activity were observed in the AL index with good ISEE 3 telemetry coverage for 11 of them. In addition, there were two small substorms outside of these intervals, both with complete observations in the distant tail. This unusual ISEE 3 data set provides a unique opportunity to test the predictions of the near-earth neutral line model. In particular, the hypothesis that energy stored in the tail lobes during the growth phase is later dissipated, in part, through the release of one or more plasmoids following expansion phase onset is examined. Clear growth phase enhancements in the lobe magnetic field intensity preceded the onsets of nine of the substorms. Plasmoids, or their lobe signatures, traveling compression regions (TCRs), were observed at ISEE 3 in association with all 11 of the major substorm intervals for which there were ISEE observations, as well as for the two small substorms. No plasmoids or TCRs were observed in the absence of substorm activity. If these ISEE 3 observations are representative, then the release of plasmoids down the tail may be a feature common to all substorms.

Slavin, J. A.↗
DOE OSTI2022

Theory of magnon polaritons in quantum Ising materials

Here, we present a theory of magnon-polaritons in quantum Ising materials, and develop a formalism describing the coupling between light and matter as an Ising system is tuned through its quantum critical point. The theory is applied to Ising materials having multilevel single-site Hamiltonians, in which multiple magnon modes are present, such as the insulating Ising magnet LiHoF 4 . We find that the magnon-photon coupling strengths may be tuned by the applied transverse field, with the coupling between the soft mode present in the quantum Ising material and a photonic resonator mode diverging at the quantum critical point of the material. A fixed system of spins will not exhibit the diamagnetic response expected when light is coupled to mobile spins or atoms. Without the diamagnetic response, one expects a divergent magnon-photon coupling strength to lead to a superradiant quantum phase transition. However, this neglects the effects of damping and decoherence present in any real system. We show that damping and decoherence may block the superradiant quantum phase transition, and lead to weak coupling between the soft magnon mode and the resonator mode. The results of the theory are applied to experimental data on the model system LiHoF 4 in a microwave resonator.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Topological and magnetic phase transitions in the bilayer Kitaev-Ising model

We investigate the phase diagram of a bilayer Kitaev honeycomb model with Ising interlayer interactions, deriving effective models via perturbation theory and performing Majorana mean-field theory calculations. We show that a diverse array of magnetic and topological phase transitions occur, depending on the direction of the interlayer Ising interaction and the relative sign of Kitaev interactions. When two layers have the same sign of the Kitaev interaction, a first-order transition from a Kitaev spin liquid to a magnetically ordered state takes place. The magnetic order points along the Ising axis and it is (anti)ferromagnetic for (anti)ferromagnetic Kitaev interactions. However, when two layers have opposite signs of the Kitaev interaction, we observe a notable weakening of magnetic ordering tendencies and the Kitaev spin liquid survives up to a remarkably larger interlayer exchange. Our mean-field analysis suggests the emergence of an intermediate gapped ℤ 2 spin-liquid state, which eventually becomes unstable upon vison condensation. The confined phase is described by a highly frustrated 120° compass model. We furthermore use perturbation theory to study the model with the Ising axis pointing along the $\hat{z}$ axis or lying in the 𝑥⁢𝑦 plane. In both cases, our analysis reveals the formation of one-dimensional Ising chains, which remain decoupled in perturbation theory, resulting in a subextensive ground-state degeneracy. Our results highlight the interplay between topological order and magnetic ordering tendencies in bilayer quantum spin liquids.

Kitaev model↗
DOE OSTI2022

Learning Planar Ising Models Software

Learning Planar Ising Models is a software package written in Matlab for learning relationships among variable in a dataset using graphical models. The software package implements a generally-applicable algorithm for learning planar Ising models from any multivariate dataset. The code provides an algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. The software includes demonstrations of the algorithm in simulations and for applications on publicly available datasets. Details of the algorithm, demonstration simulations, and applications are given in Johnson, et al; 2016. Reference: Johnson, J. K., Oyen, D., Chertkov, M., and Netrapalli, P. (2016). Learning planar Ising models. Journal of Machine Learning Research.

Oyen, Diane↗
DOE OSTI2026

Classical combinatorial optimization scaling for random Ising models on 2D heavy-hex graphs

Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum algorithms such as the quantum approximate optimization algorithm. In this study, a specific class of near term quantum computing hardware defined combinatorial optimization problems, Ising models on heavy-hex graphs both with and without geometrically local cubic terms, are examined for their classical computational hardness via empirical computation time scaling quantification. Specifically the time-to-solution (TTS) metric using the classical heuristic simulated annealing is measured for finding optimal variable assignments (ground states), as well as the time required for the optimization software Gurobi to find an optimal variable assignment. Because of the sparsity of these Ising models, the classical algorithms are able to find optimal solutions efficiently even for large instances (i.e. 100 000 spin variables). The Ising models both with and without geometrically local cubic terms exhibit average-case linear-time or weakly quadratic scaling when solved exactly using Gurobi, and the Ising models with no cubic terms show evidence of exponential-time TTS scaling when sampled using simulated annealing. These findings point to the necessity of developing and testing more complex, namely more densely connected, optimization problems in order for quantum computing to ever have a practical advantage over classical computing. Our results are another illustration that different classical algorithms can indeed have exponentially different running times, thus making the identification of the best practical classical technique important in any quantum computing vs. classical computing comparison.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Understanding and Tuning Magnetism in Layered Ising‐Type Antiferromagnet FePSe 3 for Potential 2D Magnet

Abstract Recent developments in 2D magnetic materials have motivated the search for new van der Waals magnetic materials, especially Ising‐type magnets with strong magnetic anisotropy. Fe‐based M P X 3 ( M = transition metal, X = chalcogen) compounds such as FePS 3 and FePSe 3 both exhibit an Ising‐type magnetic order, but FePSe 3 receives much less attention compared to FePS 3 . This work focuses on establishing the strategy to engineer magnetic anisotropy and exchange interactions in this less‐explored compound. Through chalcogen and metal substitutions, the magnetic anisotropy is found to be immune against S substitution for Se whereas tunable only with heavy Mn substitution for Fe. In particular, Mn substitution leads to a continuous rotation of magnetic moments from the out‐of‐plane direction toward the in‐plane. Furthermore, the magnetic ordering temperature displays non‐monotonic doping dependence for both chalcogen and metal substitutions but due to different mechanisms. These findings provide deeper insight into the Ising‐type magnetism in this important van der Waals material, shedding light on the study of other Ising‐type magnetic systems as well as discovering novel 2D magnets for potential applications in spintronics.

2D magnet↗
DOE OSTI2025

Record acceleration of the two-dimensional Ising model using a high-performance wafer-scale engine

The versatility and wide-ranging applicability of the Ising model, originally introduced to study phase transitions in magnetic materials, have made it a cornerstone in statistical physics and a valuable tool for evaluating the performance of emerging computer hardware. Here, we present a novel implementation of the two-dimensional Ising model on Cerebras Wafer-Scale Engine (WSE) – a revolutionary processor that is opening new frontiers in computing. In our deployment of the checkerboard algorithm, we optimized the Ising model to take advantage of the unique WSE architecture. Specifically, we employed a compressed bit representation storing 16 spins on each int16 word, and efficiently distributed the spins over the processing units enabling seamless weak scaling and limiting communications to only immediate neighboring units. Our implementation can handle up to 754 simulations in parallel, achieving an aggregate of over 61.8 trillion flip attempts per second for Ising models with up to 200 million spins. This represents a gain of up to 148 times over previously reported single-devices with a highly optimized implementation on NVIDIA V100 and up to 88 times in productivity compared to NVIDIA H100. Our findings highlight the significant potential of the WSE in scientific computing, particularly in the field of materials modeling.

Ising model↗
DOE OSTI2024

Paradigm for approaching the forbidden spontaneous phase transition in the one-dimensional Ising model at a fixed finite temperature

The Ising model describes collective behaviors such as phase transitions and critical phenomena in various physical, biological, economical, and social systems. It is well known that spontaneous phase transition at finite temperature does not exist in the Ising model with short-range interactions in one dimension. Yet, little is known about whether this forbidden phase transition can be approached arbitrarily closely—at fixed finite temperature. Here I use symmetry analysis of the transfer matrix to reveal the existence of spontaneous ultranarrow phase crossover (UNPC) at finite temperature in one class of one-dimensional Ising models on decorated two-leg ladders, in which the crossover temperature T 0 is determined solely by on-rung interactions and decorations, while the crossover width 2 δ T is independently, exponentially reduced ( δ T = 0 means a genuine phase transition) by on-leg interactions and decorations. These findings establish a simple ideal paradigm for realizing an infinite number of one-dimensional Ising systems with spontaneous UNPC at desirable T 0 , which would be characterized in routine laboratory measurements as a genuine first-order phase transition with large latent heat thanks to the ultranarrow δ T (say less than one nanokelvin), paving a way to push the limit in our understanding of phase transitions and the dynamical actions of frustration arbitrarily close to the forbidden regime. Published by the American Physical Society 2024

1-dimensional systems↗
DOE OSTI2025

Duality defect in a deformed transverse-field Ising model

Physical quantities with long lifetimes have both theoretical significance in the study of quantum many-body systems and practical implications for quantum technologies. In this manuscript, we investigate the roles played by topological defects in the construction of quasiconserved quantities, using as a prototypical example the Kramers-Wannier duality defect in a deformed one-dimensional quantum transverse-field Ising model. We construct the duality defect Hamiltonian in three different ways: half-chain Kramers-Wannier transformation, utilization of techniques in the Ising fusion category, and defect-modified weak integrability breaking deformation. The third method is also applicable for the study of generic integrable defects under weak integrability breaking deformations. We also work out the deformation of defect-modified higher charges in the model and study their slower decay behavior. Furthermore, we consider the corresponding duality defect twisted deformed Floquet transverse-field Ising model and investigate the stability of the isolated zero mode associated with the duality defect in the integrable Floquet Ising model, under such weak integrability breaking deformation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Machine learning force field model for kinetic Monte Carlo simulations of itinerant Ising magnets

Here, we present a scalable machine learning (ML) framework for large-scale kinetic Monte Carlo (kMC) simulations of itinerant electron Ising systems. As the effective interactions between Ising spins in such itinerant magnets are mediated by conducting electrons, the calculation of energy change due to a local spin update requires solving an electronic structure problem. Such repeated electronic structure calculations could be overwhelmingly prohibitive for large systems. Assuming the locality principle, a convolutional neural network (CNN) model is developed to directly predict the effective local field and the corresponding energy change associated with a given spin update based on Ising configuration in a finite neighborhood. As the kernel size of the CNN is fixed at a constant, the model can be directly scalable to kMC simulations of large lattices. Our approach is reminiscent of the ML force field models widely used in first-principles molecular dynamics simulations. Applying our ML framework to a square-lattice double-exchange Ising model, we uncover unusual coarsening of ferromagnetic domains at low temperatures. Our work highlights the potential of ML methods for large-scale modeling of similar itinerant systems with discrete dynamical variables.

machine learning↗
DOE OSTI2022

Successive magnetic orderings in the Ising spin chain magnet DyNi 5 Ge 3

In this report, we investigated a new rare-earth-based one-dimensional Ising spin chain magnet DyNi 5 Ge 3 by means of magnetization, specific heat, and powder neutron diffraction measurements. Due to the crystalline electrical field splitting, the magnetic Dy ions share an Ising-like ground doublet state. Owning to the local point symmetry, these Ising moments form into two canted magnetic sublattices, which were further confirmed by the angle-dependent magnetization measurement. In zero fields, two successive antiferromagnetic phase transitions were found at temperatures T N1 =6K and T N2 =5K, respectively. Only part of the moments are statically ordered in this intermediate state between T N1 and T N2 . Powder neutron diffraction experiments at different temperatures were performed as well. Further, an incommensurate magnetic propagation vector of k m =(0.5,0.4,0.5) was identified. The refined spin configurations through the irreducible representation analysis confirmed that these Ising spins are canted in the crystal ab plane.

36 MATERIALS SCIENCE↗
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↗
NASA NTRS1984

Some contributions to knowledge of the magnetospheric plasma by ISEE investigators

The ISEE project has made substantial contributions to the knowledge of the magnetosphere during the period of the IMS, especially in the discipline of Space Plasma Physics. Results obtained during approximately the first two years of the operation of ISEE-1 and -2, and touches on relevant results of ISEE-3 are reviewed. The ability to control the separation between ISEE-1 and -2, which are in nearly identical orbits, has permitted study of the motion and structure of the bow shock and magnetopause, the boundary layers, and the plasma sheet. Much evidence was obtained favoring the existence of reconnection and its relevance to the transfer of magnetic flux from the frontside to the rear of the magnetosphere, although not everyone agrees that it is the only important process. The presence of both reflected and accelerated particles was shown to lead to the development of a foreshock region between the bow shock and the interplanetary magnetic field line tangential to it.

Ogilvie, K. W.↗
NASA NTRS1984

Trajectories and orbital maneuvers for the ISEE-3/ICE comet mission

The ISEE-3/ICE spacecraft, (launched in 1978), and expected to obtain the first measurements of comet Giacobinni-Zinner in September 1985, has undertaken a combination of propulsive maneuvers, lunar swing-bys, and solar perturbations to produce its present trajectory profile. ISEE-3 is a drum-shaped, spin-stabilized spacecraft equipped with a redundant pair of high-resolution sun sensors, a medium-gain S-band antenna, a hydrazine propulsion system and a science experiment payload. After being placed into a sun-earth libration halo orbit in late 1978, ISEE-3 was retargeted to the geomagnetotail in mid-1982 and became the first spacecraft to explore the geomagnetic tail between 80 and 237 earth radii in 1983. These types of maneuvers may prove important for future scientific missions planned as follow-ons to ISEE-3/ICE, such as a joint NASA/ISAS project spacecraft scheduled for Shuttle launch in 1991, and a possible encounter with two comets in 1996 anad 1998.

Farquhar, R.↗
NASA NTRS1988

An unusual charging event on ISEE 1

Electrostatic cleanliness requirements on ISEE 1 were expected to prevent negative charging in sunlight. This has largely been true, but on three occasions, ISEE 1 has been observed to charge to significant negative potentials in sunlight. Data from the two electric field experiments and from the plasma composition experiment on ISEE 1 show that the spacecraft charged to close to -70 V in sunlight at about 0700 UT on March 17, 1978. Data from the electron spectrometer experiment show that there was a potential barrier of some -10 to -20 V about the spacecraft during this event. The potential barrier was effective in turning back emitted photoelectrons to the spacecraft. Potential barriers can be formed by differential charging on the spacecraft or by the presence of excess space charge in the plasma. The shape of the barrier suggests that it is due to the former, even though electrostatic cleanliness specifications imposed on ISEE were intended to eliminate differential charging. Modeling of this event showed that the barrier could not be produced by the presence of space charge but that it was most likely produced by differential charging of the solar arrays.

Olsen, R. C.↗