Spin Glass Research Articles

Forces on a singing wineglass rim

The characterization of friction is a multiscale problem involving a balance between asperity contacts and fluid film forces, most commonly modeled with a velocity-dependent coefficient of friction. Periodic stick–slip phenomena are often associated with the friction force that causes mechanical vibration. This type of vibration can cause noise to radiate via structural modes of a system. Notable examples include journal bearings, brake squeal, turkey calls, and wineglasses. Singing wineglasses have been used for centuries as musical instruments, so musical acousticians have studied the structural vibrations and acoustic output. However, the tri-axial force applied to the rim has not been measured. A test rig was designed to measure the vertical, tangential, and radial dynamic forces applied to the spinning glass rim and simultaneously capture the radiated noise. The sound radiated from the wineglass was observed to depend on the relative velocity at the rim and applied vertical load, so a stability region for a clear sound was determined. Additionally, the strongest radiating modes and harmonics in the pressure were found in the concurrently measured nonlinear force. This work may be extended to confirm the force measurement by existing friction models, a water medium, and more complicated systems.

On the self-overlap in vector spin glasses

We consider vector spin glass models with self-overlap correction. Since the limit of free energy is an infimum, we use arguments analogous to those for generic models to show the following: (1) the averaged self-overlap converges; (2) the self-overlap concentrates; (3) the infimum optimizes over paths whose right endpoints are the limit of self-overlap. Lastly, using these, we directly verify the equivalence between the variational formula obtained in Chen [Electron. J. Probab. 28, 1 (2023)] and Panchenko’s generalized Parisi formula in Panchenko [Ann. Probab. 46(2), 865 (2018)].

Overlap structure and free energy fluctuations in short-range spin glasses

We investigate scenarios in which the low-temperature phase of short-range spin glasses comprises thermodynamic states which are nontrivial mixtures of multiple incongruent pure state pairs. We construct a new kind of metastate supported on Gibbs states whose edge overlap values with a reference state fall within a specified range. Using this metastate we show that, in any dimension, the variance of free energy difference fluctuations between pure states within a single mixed Gibbs state with multiple edge overlap values diverges linearly with the volume. We discuss some implications of these results.

Giant magnetoresistance resulting from superzone gap in spin-frustrated rare-earth-based aluminide: DyFe2Al10.

The magnetic properties of orthorhombic aluminides have recently been the subject of investigation, revealing several intriguing phenomena within this class of materials. However, the exploration of their magnetic and electrical transport phenomena has remained somewhat limited. In this study, we delve into the magnetic and electrical transport characteristics of one such material from that group which is DyFe2Al10(DFA). Our findings go beyond classifying this material as a simple antiferromagnet; but it posses a short range ferromagnetic ordering apart from helical spin structure of Dy3+. It exhibits a metamagnetic transition and spin glass behavior below its Néel temperature (TN). Our analysis of electrical magnetotransport behavior indicates the emergence of an antiferromagnetic superzone gap, resulting in a significant enhancement in magnetoresistance effect. This discovery paves the way for a class of materials with complex interactions and notable magnetoresistance properties.

Optimization Algorithms for Multi-species Spherical Spin Glasses

This paper develops approximate message passing algorithms to optimize multi-species spherical spin glasses. We first show how to efficiently achieve the algorithmic threshold energy identified in our companion work (Huang and Sellke in arXiv preprint, 2023. arXiv:2303.12172), thus confirming that the Lipschitz hardness result proved therein is tight. Next we give two generalized algorithms which produce multiple outputs and show all of them are approximate critical points. Namely, in an r-species model we construct 2r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^r$$\\end{document} approximate critical points when the external field is stronger than a “topological trivialization" phase boundary, and exponentially many such points in the complementary regime. We also compute the local behavior of the Hamiltonian around each. These extensions are relevant for another companion work (Huang and Sellke in arXiv preprint, 2023. arXiv:2308.09677) on topological trivialization of the landscape.

Griffiths-Type Theorems for Short-Range Spin Glass Models

We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap R1,2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^{1,2}$$\\end{document} implies the non-differentiability of the two-replica free energy with respect to the replica coupling parameter λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}. In Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}_2$$\\end{document} invariant models such as the standard Edwards–Anderson model, the non-differentiability is equivalent to the spin glass order characterized by a nonzero Edwards–Anderson order parameter. This generalization of Griffiths’ theorem is proved for any short-range spin glass models with classical bounded spins. We also prove that the non-differentiability of the two-replica free energy mentioned above implies replica symmetry breaking in the literal sense, i.e., a spontaneous breakdown of the permutation symmetry in the model with three replicas. This is a general result that applies to a large class of random spin models, including long-range models such as the Sherrington-Kirkpatrick model and the random energy model. There is a 25-minute video that explains the main results of the present work:https://youtu.be/BF3hJiY1xvI

Glasslike caging with random planes.

The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics in the same way that the random energy model clarifies spin glass behavior would therefore be beneficial. Here we propose such a real-space model that is amenable to infinite-dimensional d→∞ analysis and is exactly solvable in finite d in some regimes. By joining analysis with numerical simulations, we uncover geometrical signatures of the dynamical and jamming transitions and obtain insight into the origin of activated processes. Translating these findings into the context of standard glass formers further reveals the role played by nonconvexity in the emergence of Gardner and jamming physics.

Principle of minimal singularity for Green’s functions

Analytic continuations of integer-valued parameters can lead to profound insights, such as angular momentum in Regge theory, the number of replicas in spin glasses, the number of internal degrees of freedom, the spacetime dimension in dimensional regularization, and Wilson’s renormalization group. In this work, we consider a new kind of analytic continuation of correlation functions, inspired by two recent approaches to underdetermined Dyson-Schwinger equations in D-dimensional spacetime. If the Green’s functions Gn=⟨ϕn⟩ admit analytic continuation to complex values of n, the two different approaches are unified by a novel principle for self-consistent problems: Singularities in the complex plane should be minimal. This principle manifests as the merging of different branches of Green’s functions in the quartic theories. For D=0, we obtain the closed-form solutions of the general gϕm theories, including the cases with complex coupling constant g or noninteger power m. For D=1, we derive rapidly convergent results for the Hermitian quartic and non-Hermitian cubic theories by minimizing the complexity of the singularity at n=∞. Published by the American Physical Society 2024

How microscopic epistasis and clonal interference shape the fitness trajectory in a spin glass model of microbial long-term evolution

The adaptive dynamics of evolving microbial populations takes place on a complex fitness landscape generated by epistatic interactions. The population generically consists of multiple competing strains, a phenomenon known as clonal interference. Microscopic epistasis and clonal interference are central aspects of evolution in microbes, but their combined effects on the functional form of the population’s mean fitness are poorly understood. Here, we develop a computational method that resolves the full microscopic complexity of a simulated evolving population subject to a standard serial dilution protocol. Through extensive numerical experimentation, we find that stronger microscopic epistasis gives rise to fitness trajectories with slower growth independent of the number of competing strains, which we quantify with power-law fits and understand mechanistically via a random walk model that neglects dynamical correlations between genes. We show that increasing the level of clonal interference leads to fitness trajectories with faster growth (in functional form) without microscopic epistasis, but leaves the rate of growth invariant when epistasis is sufficiently strong, indicating that the role of clonal interference depends intimately on the underlying fitness landscape. The simulation package for this work may be found at https://github.com/nmboffi/spin_glass_evodyn.

How microscopic epistasis and clonal interference shape the fitness trajectory in a spin glass model of microbial long-term evolution.

The adaptive dynamics of evolving microbial populations takes place on a complex fitness landscape generated by epistatic interactions. The population generically consists of multiple competing strains, a phenomenon known as clonal interference. Microscopic epistasis and clonal interference are central aspects of evolution in microbes, but their combined effects on the functional form of the population's mean fitness are poorly understood. Here, we develop a computational method that resolves the full microscopic complexity of a simulated evolving population subject to a standard serial dilution protocol. Through extensive numerical experimentation, we find that stronger microscopic epistasis gives rise to fitness trajectories with slower growth independent of the number of competing strains, which we quantify with power-law fits and understand mechanistically via a random walk model that neglects dynamical correlations between genes. We show that increasing the level of clonal interference leads to fitness trajectories with faster growth (in functional form) without microscopic epistasis, but leaves the rate of growth invariant when epistasis is sufficiently strong, indicating that the role of clonal interference depends intimately on the underlying fitness landscape. The simulation package for this work may be found at https://github.com/nmboffi/spin_glass_evodyn.

Low-temperature cluster spin glass transition in the single-domain NiCr2O4 nanoparticles

NiCr2O4 nanoparticles with average particle size ∼15 nm, a single-domain size maintains the bulk canted antiferromagnetic ground state, were synthesized by a microwave combustion method. The magnetic behavior was carefully investigated by static and dynamic magnetic susceptibility measurements. In addition to a spin-glass-like behavior below paramagnetic-ferrimagnetic transition at T C, the NiCr2O4 nanoparticles demonstrate a low-temperature cluster spin glass transition below the spin canting transition T S, which manifests itself as a magnetic anomaly peak around ∼12 K (at 100 Oe) in the zero-field cooled magnetization with a relatively stronger field dependence in a ‘de Almeida-Thouless’ line for spin glasses. The AC susceptibility analyses in different approaches demonstrate a larger relative peak temperature variation per frequency decade and a longer characteristic relaxation time in the order of 0.04 and 10−7 s, against 0.01 and 10−9 s for the high-temperature blocking, indicating the slow spin dynamics for the low-temperature cluster glassy phase. A field-temperature magnetic phase diagram is proposed for the single-domain NiCr2O4 nanoparticles.

Large magnetocaloric effect and exchange bias properties in Mn-Ni-Co-Sn full Heusler alloy

We have studied the structural, magnetic, magnetocaloric properties and exchange bias (EB) of a Mn-rich Mn-Ni-Co-Sn Heusler alloy, by means of the combined experimental and theoretical investigations. The alloy possesses tetragonal structure at room temperature (RT), and exhibits a first order martensitic transition at around 335 K. It also shows a large magnetocaloric effect in the vicinity of martensitic transition, with a maximum isothermal magnetic entropy change of around 35 J/kg.K, which is significantly larger than that reported for many other Heusler systems. Frequency dependence of spin freezing temperature obeying the dynamical scaling and Vogel-Fulcher law, along with the memory effect confirms the presence of cluster spin glass (CSG) state at low temperatures in the alloy. It shows EB effect at low temperatures, with a maximum EB field of 0.099 Tesla at 2 K, after field cooling in presence of 1 Tesla. Strong exchange coupling among the CSG clusters embedded in a strong ferrimagnetic matrix is found to be responsible for the observed EB. Ab-initio calculations using density functional theory on a representative Mn50Ni35.94Co6.25Sn7.81 alloy (very close to our experimental composition) shows the tetragonal structure with the ferrimagnetic ordering as the ground state, which is in good agreement with the experimental results. Exchange mechanism behind the observed EB in the present alloy has been discussed in the light of varying interatomic distances between different atomic pairs, and hence the magnetic coupling.

Griffiths-like behavior and magnetocaloric properties of rare-earth silicide Tb2Co0.8Si3.2

Novel rare-earth silicide, Tb2Co0.8Si3.2 compound, crystallizes in Lu2CoGa3 structure, a distorted substitution variant of the AlB2 structure. The compound exhibits a complex magnetic state, with a ferromagnetic transition at 58 K, followed by successive antiferromagnetic transitions at 24 K and 8 K, respectively. Isothermal and magnetic hysteresis studies indicate the prominence of competing antiferro and ferromagnetic interactions in the compound. However, this does not lead to the formation of spin glass behavior, as confirmed by AC magnetic susceptibility and heat capacity studies. In the paramagnetic state, the short-range ferromagnetic ordering of cobalt creates a Griffiths-like anomaly that is suppressed at higher magnetic fields. Investigation of magnetocaloric and magnetoresistance properties identifies the compound as a conventional second-order magnetocaloric material with negative magnetoresistance. Furthermore, the determination of Landau coefficients and subsequent analysis indicate that the isothermal entropy change of the compound can be calculated from these coefficients.

Room temperature polaritonic soft-spin XY Hamiltonian in organic–inorganic halide perovskites

Abstract Exciton–polariton condensates, due to their nonlinear and coherent characteristics, have been employed to construct spin Hamiltonian lattices for potentially studying spin glass, critical dephasing, and even solving optimization problems. Here, we report the room-temperature polariton condensation and polaritonic soft-spin XY Hamiltonian lattices in an organic–inorganic halide perovskite microcavity. This is achieved through the direct integration of high-quality single-crystal samples within the cavity. The ferromagnetic and antiferromagnetic couplings in both one- and two-dimensional condensate lattices have been observed clearly. Our work shows a nonlinear organic–inorganic hybrid perovskite platform for future investigations as polariton simulators.

Observation of Topological Hall Effect in a Chemically Complex Alloy.

The topological Hall effect (THE) is the transport response of chiral spin textures and thus can serve as a powerful probe for detecting and understanding these unconventional magnetic orders. So far, the THE is only observed in either noncentrosymmetric systems where spin chirality is stabilized by Dzyaloshinskii-Moriya interactions, or triangular-lattice magnets with Ruderman-Kittel-Kasuya-Yosida-type interactions. Here, a pronounced THE is observed in a Fe-Co-Ni-Mn chemically complex alloy with a simple face-centered cubic (fcc) structure across a wide range of temperatures and magnetic fields. The alloy is shown to have a strong magnetic frustration owing to the random occupation of magnetic atoms on the close-packed fcc lattice and the direct Heisenberg exchange interaction among atoms, as evidenced by the appearance of a reentrant spin glass state in the low-temperature regime and the first principles calculations. Consequently, THE is attributed to the nonvanishing spin chirality created by strong spin frustration under the external magnetic field, which is distinct from the mechanism responsible for the skyrmion systems, as well as geometrically frustrated magnets.

Spin glass states in multicomponent layered perovskites

Temperature-dependent dc-magnetization and ac-susceptibility curves have been recorded for series of single and double layered Ruddlesden-Popper multicomponent perovskites with chemical formula A2BO4 and A3B2O7, respectively, with (La, Sr) on A-sites and up to 7 different cations on the B-sites (Ti, Cr, Mn, Fe, Co, Ni, Cu). The phase purity and chemical homogeneity of the compounds were investigated by X-ray diffraction and energy dispersive X-ray spectroscopy. Independently of the composition, spin glassiness is observed in both systems. Scaling analyses suggest the materials undergo spin glass phase transitions at low temperatures. Yet, qualitative differences are observed between the single-layered and double-layered systems, which are discussed in the light of the spatial dimensionality and magnetic interaction in layered oxide perovskites.

Revelation of the high hardness and spin glass behavior in the novel magnetic material CrFeB

Ternary transition metal borides (TTMBs) will break materials application limitation in harsh service environments, owing to their structure versatility and high component tunable ability. Herein, we reported a solid solution boride CrFeB synthesized by high pressure and high temperature method. CrFeB yields an asymptotic hardness of 14.2 GPa and thermal stability temperature is up to 1250 K. DC magnetic susceptibility measurements revealed that there is a separation between zero-field cooled and field cooled curve at around 5 K, which indicated the spin glass behavior for CrFeB. Temperature dependence AC susceptibility analysis gives further evidence that the freezing temperature increases with frequency following Vogel-Fulcher law. On the basis of XPS results and first-principle calculations, we speculate that the complex magnetic behaviors may derive from the short-range magnetic exchange of same occupation sites two metal atoms. Cr and Fe atoms tend to have opposite magnetic moments in these short-range exchange behaviors. The intrinsic magnetic disorder and short-range frustration lead to spin random freezing of CrFeB at low temperatures, which conforms to typical spin glass characteristics. These results will contribute to understanding the complex magnetism behavior of CrFeB and provides a new idea to design multifunctional TTMBs.

Spin glass state in Co doped NdMnO3

The temperature-dependent ac susceptibility studies of in-phase component (χ′ac) and out of phase component (χac″) was done on a single phase polycrystalline NdMn0.6Co0.4O3 sample. The measurements were conducted in 4 Oe ac field and 0 Oe dc field at frequencies of 111, 311, 1011, and 1311 Hz. As the frequency increases, the magnitude of χ′ac decreases, and its peak position, corresponding to Tf, moves towards higher temperatures. This strongly suggests the presence of a spin glass (SG) state and the absence of long-range ferromagnetic ordering. The value of relative shift in freezing temperature (δTf) is found to be δTf = 0.0089, which suggests the existence of canonical SG state in NdMn0.6Co0.4O3 sample. To confirm it the ac susceptibility data was further analyzed using Arrhenius, Vogel Fulcher, and Power–law.

Entropy and dimension spectrum of the mean-field spin glass model

A self-contained new constructive solution of the mean-field Sherrington-Kirkpatric spin-glass model is obtained from the study of the behaviour of the entropy of the Gibbs measure at low temperatures.

Magnetic field-induced narrow first-order and metamagnetic phase transitions of Nd5Ge3

We report on the magnetic behaviour of Nd5Ge3 by investigating through magnetization, neutron diffraction and muon spin relaxation measurements. Temperature dependent-magnetization, muon depolarization rate (λ), initial asymmetry (A0) and the stretched exponent (β) show a clear anomaly at the Néel temperature TN ∼ 54 K. However, the short-range correlated ferromagnetic interactions below TN are inferred from the diffuse scattering mechanism as revealed by zero-field neutron diffraction data. Narrow first order phase transition is due to the competing interaction of a high temperature weak-antiferromagnetic and low temperature glassy states. Magnetic field-induced reentrant spin glass state from a magnetic glass state is observed, before it transforms to a ferromagnetic state.