Ising System Research Articles

Dynamic magnetic hysteresis features of a mixed spin (2, 5/2) Ising system on a hexagonal lattice under an oscillating magnetic field within the path probability method

Recently, we [J. Magn. Magn. Mater. 514 (2020) 167242] presented a study of the dynamic magnetic loop features of molecular-based magnetic materials and ferrimagnetism that were investigated by using a mixed spin 1/2 and spin-1 ferrimagnetic Ising system within the path probability method. We found several interesting dynamic magnetic hysteresis properties and observed that the obtained results are in qualitatively good agreement with some theoretical and experimental studies in magnetic materials. We extended our recent previous published work to study the dynamic magnetic hysteresis properties of molecular-based magnetic materials and ferrimagnetism utilizing the mixed spin (2, 5/2) ferrimagnetic Ising system on a hexagonal lattice employing the path probability method. The spin (2, 5/2) Ising system is one of the most suitable and most used prototypical systems to investigate many molecular-based magnetic materials and ferrimagnetic materials. We found more interesting dynamic magnetic hysteresis properties such as double, triple, quadruple and quintuple loop behaviors for the layer magnetization, and only double and triple loops for the total magnetization. We found that some of our obtained results are in qualitatively good agreement with some theoretical, experimental reported works, and the works on some magnetic materials as obtained by the melt-spinning technique.

Designing Ising machines with higher order spin interactions and their application in solving combinatorial optimization

The Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have recently been proposed as a potential candidate for solving COPs, with the promise of significant performance benefit. However, prior work on designing dynamical systems as Ising machines has primarily considered quadratic interactions among the nodes. Dynamical systems and models considering higher order interactions among the Ising spins remain largely unexplored, particularly for applications in computing. Therefore, in this work, we propose Ising spin-based dynamical systems that consider higher order (> 2) interactions among the Ising spins, which subsequently, enables us to develop computational models to directly solve many COPs that entail such higher order interactions (i.e., COPs on hypergraphs). Specifically, we demonstrate our approach by developing dynamical systems to compute the solution for the Boolean NAE-K-SAT (K ≥ 4) problem as well as solve the Max-K-Cut of a hypergraph. Our work advances the potential of the physics-inspired ‘toolbox’ for solving COPs.

Dynamic study of a ternary trilayer Ising system with crystal field interaction

Dynamic study of a ternary trilayer Ising system with crystal field interaction

Phase transitions of a mixed spin ferrimagnet in high temperatures

In this research paper molecular mean-field theory (MMFT) has been investigated based on Gibbs-Bogoliubov free energy function of a ferrimagnetics mixed spin-3 and spin-5/2 Blume-Capel model with different magnetic crystal fields. The free energy of the proposed ferrimagnet has been evaluated depending on the trial Hamiltonian operator. Minimizing the free energy, one may induce characteristic features of the longitudinal magnetizations, phase transitions and spin compensation temperatures, in the ranges of low temperatures, respectively. In particular, we study the effect of crystal field domains on the critical phenomena for the proposed model. The sublattice magnetization dependence of free energy function has been discussed as well. Our results predict the existence of multiple spin compensation sites in the disordered Blume-Capel Ising system for a simple cubic lattice.

Experimental critical dynamics of 3-methyl pyridine/D2O mixtures without and with antagonistic salt

We observed criticality in the structure and dynamics of a three-dimensional (3D) and two-dimensional (2D) Ising system consisting of 3-methyl pyridine $\text{(3MP)}/{\mathrm{D}}_{2}\mathrm{O}$ without and with antagonistic salt. We could describe both dynamic criticalities by the Kawasaki crossover function. The dynamic critical exponent was $z=0.063\ifmmode\pm\else\textpm\fi{}0.020$ and $0.005\ifmmode\pm\else\textpm\fi{}0.019$ for three and two dimensions, which confirms earlier observations in the 3D case and confirms expectations in the 2D case. The amplitudes of the critical dynamics are governed by the bare viscosities experimentally, and by the coefficient $R$ theoretically [the latter is proportional to ${(4\ensuremath{-}d)}^{\ensuremath{-}1}$ with the dimensionality $d$]. This finding is in accordance with the lubrication effect [N. Gov, A. G. Zilman, and S. Safran, Phys. Rev. E 70, 011104 (2004)], which is also connected to lamellar systems of the Brazovskii criticality [M. Gvaramia et al., Colloid Polym. Sci. 297, 1507 (2019)]. This lubrication effect is tightly connected to a laminar flow enforced by the domain structure, and it also holds for our 2D Ising system. The experimental techniques employed were small-angle neutron and x-rays scattering for the static criticality, and dynamic light scattering and neutron spin echo spectroscopy for the critical dynamics. Furthermore, the criticality of the viscosities was measured.

Finite-Temperature Avalanches in 2D Disordered Ising Models

We study the qualitative and quantitative properties of the Barkhausen noise emerging at finite temperatures in random Ising models. The random-bond Ising Model is studied with a Wolff cluster Monte-Carlo algorithm to monitor the avalanches generated by an external driving magnetic field. Satisfactory power-law distributions are found which expand over five decades, with a temperature-dependent critical exponent which matches the existing experimental measurements. We also focus on a Ising system in which a finite fraction of defects is quenched. Also the presence of defects proves able to induce a critical response to a slowly oscillating magnetic field, though in this case the critical exponent associated with the distributions obtained with different defect fractions and temperatures seems to belong to the same universality class, with a critical exponent close to 1.

Mean and Gaussian curvatures of equilibrium states for a spin-1 Ising system: existence of minimal surface in the paramagnetic solutions

Mean and Gaussian curvatures of equilibrium states for a spin-1 Ising system: existence of minimal surface in the paramagnetic solutions

Residual entropy of a two-dimensional Ising model with crossing and four-spin interactions

We study the residual entropy of a two-dimensional Ising model with crossing and four-spin interactions, both in the case of a zero magnetic field and in an imaginary magnetic field iπ/2kBT. The spin configurations of this Ising model can be mapped into the hydrogen configurations of square ice with the defined standard direction of the hydrogen bonds. Making use of the equivalence of this Ising system with the exactly solved eight-vertex model and taking the low temperature limit, we obtain the residual entropy. Two soluble cases in the zero field and one soluble case in the imaginary field are examined. In the case that the free-fermion condition holds in zero field, we find that the ground states in the low temperature limit include the configurations disobeying the ice rules. In another case in zero field where the four-spin interactions are −∞ and another case in imaginary field where the four-spin interactions are 0, the residual entropy exactly agrees with the result of square ice determined by Lieb in 1967. In the solutions to the latter two cases, we have shown alternative approaches to the residual entropy problem of square ice.

Phase separation kinetics of binary mixture in the influence of bond disorder: sensitivity to quench temperature

ABSTRACT Morphologies in phase-separating systems can significantly influence final material properties. We present extensive Monte Carlo simulation results on segregation kinetics of critical binary mixture (-Ising system) with a fraction of bond disorder introduced regularly. The effect of various quench temperatures is studied on growth kinetics and scaling properties of evolved morphologies. The morphology changes from their usual bicontinuous isotropic patterns at zero disorder to short strips and lamellar patterns (anisotropy) with the increasing disorder at shallow quench depth. The domain evolution at lower disorder remains at a transient growth regime for deep quench; however, the lamellar pattern is observed at high disorder for the same quench depth. The scaling behavior changes significantly with quench depths at the higher fraction of disorder. Though, a tiny deviation is observed at lower disorder fractions for shallow quench depths. The length scale freezes () to finite size at the higher disorder asymptotically.

Hybrid spin Hall nano-oscillators based on ferromagnetic metal/ferrimagnetic insulator heterostructures

Spin-Hall nano-oscillators (SHNOs) are promising spintronic devices to realize current controlled GHz frequency signals in nanoscale devices for neuromorphic computing and creating Ising systems. However, traditional SHNOs devices based on transition metals have high auto-oscillation threshold currents as well as low quality factors and output powers. Here we demonstrate a new type of hybrid SHNO based on a permalloy (Py) ferromagnetic-metal nanowire and low-damping ferrimagnetic insulator, in the form of epitaxial lithium aluminum ferrite (LAFO) thin films. The superior characteristics of such SHNOs are associated with the excitation of larger spin-precession angles and volumes. We further find that the presence of the ferrimagnetic insulator enhances the auto-oscillation amplitude of spin-wave edge modes, consistent with our micromagnetic modeling. This hybrid SHNO expands spintronic applications, including providing new means of coupling multiple SHNOs for neuromorphic computing and advancing magnonics.

Spin dynamics of quantum Ising chain in random correlated magnetic fields

The spin dynamics of one-dimensional quantum Ising chain with random correlated magnetic fields (RCMFs) is studied at the high-temperature limit by the recursion method. Both the spin autocorrelation function and its corresponding spectral density are investigated under the circumstance of bimodal-type and Gaussian-type RCMFs. It is found that the dynamics of the system are highly dependent on the correlated mode and strength between the longitudinal and transverse magnetic fields (i.e., Bxi and Bzi). Due to the cooperation or synergy effect between Bxi and Bzi, crossovers between different dynamical behaviors can be revealed in most of the cases. In general, the dynamics of the system is dominant by the field (Bxi or Bzi) with a larger proportion when the RCMFs are weak. However, when the RCMFs are strong, the system tends to exhibit a disordered behavior, which manifests as a multiple-peak feature in the bimodal-type case or a broaden spectral in the Gaussian-type case. In another perspective, when the proportion of Bzi is small, the central-peak behavior can be enhanced by increasing the proportion of Bxi. Interestingly, when the proportion of Bzi is large, the perturbation of Bxi on Bzi tends to excite new dynamical behavior. Our results indicate that using RCMF to manipulate the spin dynamics of the Ising system may be a new try.

Activity and steady‐state kinetics of one‐dimensional kinetic Ising model

AbstractIn this work, we focused on the kinetics of a one‐dimensional Ising system (1DIS) with constant nearest‐neighbor interaction (NNI). The exact solution of both thermodynamics and kinetics of this system under quasi‐chemical approximation (QCA) had been shown in the literature, and the equilibrium solution was exact. In this work, it was discussed why QCA applied the best in the case of 1DIS with constant NNI. Furthermore, extension had been made to discuss that due to this special reason, perhaps the kinetics of the system under QCA is the correct steady‐state kinetics. Inspired by this observation, the activity and activity coefficients of the system was studied closely to re‐examine the form of the equation of motion under QCA. A novel concept—the instantaneous activities and the corresponding instantaneous activity coefficients—was introduced, and in terms of these quantities the kinetics seemed to be much simpler and physically more meaningful. The chevron plot of this system was also discussed and new way of looking at the rollover of chevron plots was presented.

Frustrated Magnetism: A Case Study of Geometric Frustration

In this research work, frustrations arising from the geometries of triangular lattices have been studied with the aid of Ising and Heisenberg models. The study reveals that geometrical frustrations can generate multiple degeneracies in the ground state. The quantum spin flip terms in the Heisenberg model are observed to play a vital role in the partial lifting up of these degeneracies. Hence, multiple degeneracies as consequence of frustrations are more pronounced for the Ising systems, which are devoid of quantum fluctuations. The observed six- and four-fold ground state degeneracies at zero field for three spins Ising and Heisenberg systems respectively are broken down to half at finite longitudinal fields. For this three-spin system, quantum phase transitions (QPT) are observed at critical longitudinal fields of J and 1.5J respectively for the Ising and Heisenberg models. At these critical fields, the ground states are observed to shift from quasi-antiferromagnet to ferromagnet. However, for the Heisenberg three-spin system in the presence of a transverse field, no transition is observed.

Dynamic magnetic properties of spin-7/2 multilayer Ising system in an oscillating magnetic field

ABSTRACT We studied the dynamic magnetic properties such as dynamic phase transitions, dynamic compensation temperatures, and dynamic phase diagrams in the spin-7/2 multilayer Ising system under an oscillating external magnetic field The system was simulated in the mean-field approximation using a Glauber type stochastic dynamic. The mean sublattice magnetizations’ time variations were examined to determine the system's dynamic phases. The thermal behavior of dynamic sublattice magnetizations was investigated to determine the type of dynamic phase transitions (first- or second-order) and to obtain the dynamic compensation temperatures. and type compensating behaviors were seen in various types of magnetization curves. The phase diagrams are calculated in and planes, for different values of the Hamiltonian parameters. The p, i, f1/2 , f7/2 , af7/2 , and af1/2 fundamental phases, as well as the i + p, i + f1/2 , af1/2 + p, af7/2 + p and i + af1/2 mixed phases. The system illustrated one, two, or three dynamic critical points (•) and E, TP, Z, and B special points.

Crystallinity of the Homogenized Energy Density of Periodic Lattice Systems

We study the homogenized energy densities of periodic ferromagnetic Ising systems. We prove that, for finite range interactions, the homogenized energy density, identifying the effective limit, is crystalline, i.e., its Wulff crystal is a polytope, for which we can (exponentially) bound the number of vertices. This is achieved by deriving a dual representation of the energy density through a finite cell formula. This formula also permits easy numerical computations: we show a few experiments where we compute periodic patterns which minimize the anisotropy of the surface tension.

E-Spin: A Stochastic Ising Spin Based on Electrically-Controlled MTJ for Constructing Large-Scale Ising Annealing Systems

With its unique computer paradigm, the Ising annealing machine has become an emerging research direction. The Ising annealing system is highly effective at addressing combinatorial optimization (CO) problems that are difficult for conventional computers to tackle. However, Ising spins, which comprise the Ising system, are difficult to implement in high-performance physical circuits. We propose a novel type of Ising spin based on an electrically-controlled magnetic tunnel junction (MTJ). Electrical operation imparts true randomness, great stability, precise control, compact size, and easy integration to the MTJ-based spin. In addition, simulations demonstrate that the frequency of electrically-controlled stochastic Ising spin (E-spin) is 50 times that of the thermal disturbance MTJ-based spin (p-bit). To develop a large-scale Ising annealing system, up to 64 E-spins are implemented. Our Ising annealing system demonstrates factorization of integers up to 264 with a temporal complexity of around O(n). The proposed E-spin shows superiority in constructing large-scale Ising annealing systems and solving CO problems.

The high-Q static scattering of 3-methyl pyridine/D2O mixtures without and with antagonistic salt

Here we focus on the high-Q small-angle neutron scattering where we observed deviations from an ideal power law Q−2. From theory, this deviation Δ arises from the critical correlation-function exponent ηd in d dimensions. The investigated systems were 3-methyl pyridine/D2O without and with antagonistitc salt. They display the critical behavior of a 3d and 2d Ising system, respectively. In the first case, the value of Δ matches the ideal value η3 well, but in the latter case the value of Δ is affected by the two confined dimensions and the third dimension.

Swarm-like ground-state searching based on a path-integral quantum Monte Carlo method for automatically fluctuation-controlled simulated annealing

The path-integral quantum Monte Carlo (PIQMC) method is widely used as a classical simulation algorithm for quantum annealing. Replicas represent different points in imaginary time. We propose and demonstrate a swarm-like ground-state searching algorithm based on the PIQMC method for automatically fluctuation-controlled simulated annealing. Replicas help one another to search for the ground state of an Ising system as if forming a swarm and working cooperatively. Their interactions are local, simple and fluctuate to a certain degree. Such fluctuations are necessary to escape local minima, but the fluctuations do not need to be explicitly controlled. The size of fluctuations is automatically adjusted as annealing proceeds. We solve max-cut problems for algorithm evaluation, each of which corresponds to a graph of 100 vertices. We also solve the same problems using a conventional method based on the Metropolis algorithm for comparison.

Correlation between the In-Plane Critical Behavior and Out-of-Plane Interaction of Ternary Lipid Membranes.

Liquid-liquid phase-separating lipid membranes belong to the 2-D Ising universality class. While their in-plane critical behaviors are well studied, how the behaviors modulate out-of-plane interactions is rarely explored, despite its profound implications for biomembranes and 2-D ferromagnets. Here, we examine how the interlayer interaction, manifested as membrane fusion, is affected by the membranes' critical fluctuations. Remarkably, the critical fluctuations suppress membrane fusion, suggesting a correlation between critical behaviors and interlayer interactions for 2-D Ising systems.

Calculation of the Free Energy of the Ising Model on a Cayley Tree via the Self-Similarity Method

In this study, an interactive Ising model having the nearest and prolonged next-nearest neighbors defined on a Cayley tree is considered. Inspired by the results obtained for the one-dimensional Ising model, we will construct the partition function and then calculate the free energy of the Ising model having the prolonged next nearest and nearest neighbor interactions and external field on a two-order Cayley tree using the self-similarity of the semi-infinite Cayley tree. The phase transition problem for the Ising system is investigated under the given conditions.