Ising Model Research Articles

Research on Ship Collision Risk Calculation in Port Navigation Waters Based on Ising Model and AIS Data

Research on Ship Collision Risk Calculation in Port Navigation Waters Based on Ising Model and AIS Data

Deciphering a Million-Plus RSA Integer with Ultralow Local Field Coefficient h and Coupling Coefficient J of the Ising Model by D-Wave 2000Q

Deciphering a Million-Plus RSA Integer with Ultralow Local Field Coefficient h and Coupling Coefficient J of the Ising Model by D-Wave 2000Q

Wetting and emergence of long-range couplings in arrays of fluid cells

Critical wetting is of crucial importance for the phase behavior of a simple fluid or Ising magnet confined between walls that exert opposing surface fields so that one wall favors liquid (spin up), while the other favors gas (spin down). We show that arrays of boxes filled with fluid and linked by channels with appropriately chosen opposing walls can exhibit long-range cooperative effects on a length scale far exceeding the bulk correlation length. We give the theoretical foundations of these long-range couplings by using a lattice gas (Ising model) description of a system. Published by the American Physical Society 2024

Bayesian finite mixtures of Ising models

Bayesian finite mixtures of Ising models

Topologically Defective Lattice Potential‐Based Gain‐Dissipative Ising Annealer with Large Noise Margin

AbstractGain‐dissipative Ising machines (GIMs) are annealers inspired by physical systems such as Ising spin glasses to solve combinatorial optimization problems. Compared to traditional quantum annealers, GIM is relatively easier to scale and can save on additional power consumption caused by low‐temperature cooling. However, traditional GIMs have a limited noise margin. Specifically, their normal operation requires ensuring that the noise intensity is lower than their saturation fixed point amplitude, which may result in increased power consumption to suppress noise‐induced spin state switching. To enhance the noise robustness of GIM, in this study a GIM based on a topologically defective lattice potential (TDLP) is proposed. Numerical simulations demonstrate that the TDLP‐based GIM can accurately simulate the bifurcation spin evolution in the Ising model. Furthermore, through the MAXCUT benchmark based on G‐set graphs, the optimal performance of TDLP‐based GIM is shown to surpass that of traditional GIMs. Additionally, the proposed TDLP‐based GIM successfully solves the MAXCUT benchmark and domain clustering dynamics benchmark based on G‐set graphs when the noise intensity exceeds its saturation fixed‐point amplitude. This indicates that the proposed system provides a promising architecture for breaking the small noise constraints required by traditional GIMs.

Biased Ising Model Using Two Coupled Kerr Parametric Oscillators with External Force

Biased Ising Model Using Two Coupled Kerr Parametric Oscillators with External Force

Variational denoising for variational quantum eigensolver

The variational quantum eigensolver (VQE) is a hybrid algorithm that has the potential to provide a quantum advantage in practical chemistry problems that are currently intractable on classical computers. VQE trains parameterized quantum circuits using a classical optimizer to approximate the eigenvalues and eigenstates of a given Hamiltonian. However, VQE faces challenges in task-specific design and machine-specific architecture, particularly when running on noisy quantum devices. This can have a negative impact on its trainability, accuracy, and efficiency, resulting in noisy quantum data. We propose variational denoising, an unsupervised learning method that employs a parameterized quantum neural network to improve the solution of VQE by learning from noisy VQE outputs. Our approach can significantly decrease energy estimation errors and increase fidelities with ground states compared to noisy input data for the H2, LiH, and BeH2 molecular Hamiltonians and the transverse field Ising model. Surprisingly, it only requires noisy data for training. Variational denoising can be integrated into quantum hardware, increasing its versatility as an end-to-end quantum processing for quantum data. Published by the American Physical Society 2024

Critical Exponents and Universality for Fractal Time Processes above the Upper Critical Dimensionality

We study the critical behaviors of systems undergoing fractal time processes above the upper critical dimension. We derive a set of novel critical exponents, irrespective of the order of the fractional time derivative or the particular form of interaction in the Hamiltonian. For fractal time processes, we not only discover new universality classes with a dimensional constant but also decompose the dangerous irrelevant variables to obtain corrections for critical dynamic behavior and static critical properties. This contrasts with the traditional theory of critical phenomena, which posits that static critical exponents are unrelated to the dynamical processes. Simulations of the Landau–Ginzburg model for fractal time processes and the Ising model with temporal long-range interactions both show good agreement with our set of critical exponents, verifying its universality. The discovery of this new universality class provides a method for examining whether a system is undergoing a fractal time process near the critical point.

Work statistics for quantum spin chains: Characterizing quantum phase transitions, benchmarking time evolution, and examining passivity of quantum states

We study three aspects of work statistics in the context of the fluctuation theorem for quantum spin chains up to 1024 sites by numerical methods based on matrix-product states (MPSs). First, we use our numerical method to evaluate the moments/cumulants of work done by the sudden quench process on the Ising or Haldane spin chains, and we study their behaviors across the quantum phase transitions. Our results show that, up to the fourth cumulant, the work statistics can indicate the quantum phase transition characterized by the local order parameters but barely for purely topological phase transitions. Second, we propose to use the fluctuation theorem, such as Jarzynski's equality, which relates the real-time correlator to the ratio of the thermal partition functions, as a benchmark indicator for the numerical real-time evolving methods. Third, we study the passivity of ground and thermal states of quantum spin chains under some cyclic impulse processes. We show that the passivity of thermal states and ground states under the Hermitian actions is ensured by the second laws and variational principles, respectively, and we also verify this by numerical calculations. In addition, we also consider the passivity of ground states under non-Hermitian actions, for which the variational principle cannot be applied. Despite that, we find no violation of passivity from our numerical results for all the cases considered in the Ising and Haldane chains. Overall, we demonstrate that the work statistics for the sudden quench and impulse processes can be evaluated precisely by the numerical MPS method to characterize quantum phase transitions and examine the passivity of quantum states. We also propose to exploit the universality of the fluctuation theorem to benchmark the numerical real-time evolutions in an algorithmic and model-independent way. Published by the American Physical Society 2024

Quantum critical fluctuations in a transverse-field Ising magnet

CoNb2O6 is a model system for a spin-1/2 one-dimensional (1D) transverse-field Ising magnet (TFIM) with a rather low three-dimensional (3D) Néel ordering temperature at TN=2.95 K. We studied CoNb2O6 using ultrasound measurements down to 0.3 K in transverse magnetic fields applied along the b direction. Upon entering the 3D ordered state, we observe pronounced anomalies in the transverse acoustic mode c 66. In particular, from 1.3 to 1.5 K and around 4.7 T, this mode reveals an almost diverging softening, which is considerably reduced at lower and higher magnetic fields. We interpret this as an influence of quantum critical fluctuations emerging from the quantum critical point (QCP) of the 1D Ising spin chains at about 4.75 T, which lies below the QCP of the 3D ordering at about 5.4 T. This is clear experimental evidence of the predicted generic phase diagram for a TFIM with superimposed 3D ordering.

Exploration of dynamic phase transition of 3D Ising model with a new long-range interaction by using the Monte Carlo method

In this paper, we present a novel interpretation of the long-range interaction for exploring the magnetic characteristics of the 3D Ising model. To describe the long-range interaction, we utilize spin chains, which enable us to explore the dynamic magnetic behaviors of this model. The research investigates the impacts of the amplitude of the time-dependent magnetic field h0 and period τ on the dynamic phase transition by obtaining phase diagrams and midplane cross-sections of the system. Critical exponents are also discussed, which are consistent with other theoretical results. The dynamic hysteresis behaviors are then examined through various physical parameters. As the temperature increases, the area and shape of the dynamic hysteresis loop change. Our theoretical conclusions are consistent with those of other theoretical and experimental studies.

Coupled parametric oscillators: From disorder-induced current to asymmetric Ising model

We study the effects of the interplay of weak disorder and weak coupling in a system of parametric micromechanical oscillators. Each oscillator is bistable, enabling the mapping of its stable states onto spin states. The coupling changes the rate of interstate switching of an oscillator depending on the state of other oscillators. We demonstrate that the change is exponentially strong and therefore manifests even for weak coupling. Difference in the oscillator eigenfrequencies translates into disorder in the system. The analysis and the experiment show that disorder leads to a nontrivial stationary state that displays current. The system provides a well-controlled and fully characterized implementation of the asymmetric Ising model, in which coupled spins affect each other differently. This model plays an important role in physics and biology. Our findings open the possibilities of constructing and exploring asymmetric Ising systems with controlled parameters and connectivity. Published by the American Physical Society 2024

Error estimation in current noisy quantum computers

One of the main important features of the noisy intermediate-scale quantum (NISQ) era is the correct evaluation and consideration of errors. In this paper, we analyse the main sources of errors in current (IBM) quantum computers and we present a useful tool (TED-qc) designed to facilitate the total error probability expected for any quantum circuit. We propose this total error probability as the best way to estimate a lower bound for the fidelity in the NISQ era, avoiding the necessity of comparing the quantum calculations with any classical one. In order to contrast the robustness of our tool we compute the total error probability that may occur in three different quantum models: 1) the Ising model, 2) the Quantum-Phase Estimation (QPE), and 3) the Grover’s algorithm. For each model, the main quantities of interest are computed and benchmarked against the reference simulator’s results as a function of the error probability for a representative and statistically significant sample size. The analysis is satisfactory in more than the 99%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$99\\%$$\\end{document} of the cases. In addition, we study how error mitigation techniques are able to eliminate the noise induced during the measurement. These results have been calculated for the IBM quantum computers, but both the tool and the analysis can be easily extended to any other quantum computer.

Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field

Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field

Magnetic properties of a ferrimagnetic transverse Ising system on the multilayer kagome-like lattice

Based on the Trotter-Suzuki formula, the transverse Ising model is proposed to investigate the magnetic properties of a ferrimagnetic multilayer kagome-like lattice by Monte Carlo simulation. When different parameters are considered, the rich magnetization profiles and the multi-loop hysteresis behaviors are observed. It is found that there is a small peak in the transverse magnetization curve, which is related to the phase transition temperature.

The two upper critical dimensions of the Ising and Potts models

We derive the exact actions of the Q-state Potts model valid on any graph, first for the spin degrees of freedom, and second for the Fortuin-Kasteleyn clusters. In both cases the field is a traceless Q-component scalar field Φα. For the Ising model (Q = 2), the field theory for the spins has upper critical dimension \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{\ ext{c}}}^{{\ ext{spin}}}$$\\end{document} = 4, whereas for the clusters it has \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{\ ext{c}}}^{{\ ext{cluster}}}$$\\end{document} = 6. As a consequence, the probability for three points to be in the same cluster is not given by mean-field theory for d within 4 < d < 6. We estimate the associated universal structure constant as \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C=\\sqrt{6-d}+\\mathcal{O}{\\left(6-d\\right)}^{3/2}$$\\end{document}. This shows that some observables in the Ising model have an upper critical dimension of 4, while others have an upper critical dimension of 6. Combining perturbative results from the ϵ = 6 – d expansion with a non-perturbative treatment close to dimension d = 4 allows us to locate the shape of the critical domain of the Potts model in the whole (Q, d) plane.

Spin textures of coherent photons with SU(4) symmetry

We show coherent photons with spin and orbital angular momentum have symmetry of special unitary group of degree four, SU(4), both theoretically and experimentally. We show the degree of polarisation could be a measure to characterise the quantum coherency of a spin state, which was significantly affected by the partial trace out of orbital degree of freedom. By changing the amplitudes of the classically entangled state, we observed a crossover from quantum Heisenberg spin to classical Ising spin. We also demonstrated projections of coherent states, which recover the coherency of the spin state, while the SU(4) state is projected to be a simple product state of SU(2)×SU(2). Based on the developed platform, we have explored spin texture of coherent photons, and found a unique spin profile reminiscent of the Bengal cat upon wrapping to a three-dimensional sphere. We have controlled the phase between singlet and triplet states and found the spin texture rotated upon increasing the phase.

Dually Weighted Multi-matrix Models as a Path to Causal Gravity-Matter Systems

AbstractWe introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model corresponds to the CDT-matrix model introduced by Benedetti and Henson (Phys Lett B 678:222, 2009). We present exact as well as approximate results for the Gaussian averages of characters of a Hermitian matrix A and $$A^2$$ A 2 for a given representation and establish the present limitations that prevent us to solve the model analytically. This sets the stage for the formulation of more sophisticated matter models coupled to two-dimensional CDT as dually weighted multi-matrix models providing a complementary view to the standard simplicial formulation of CDT-matter models.

Nonperturbative thermodynamic extrinsic curvature of the anyon gas

Thermodynamic extrinsic curvature is a new mathematical tool in thermodynamic geometry. By using the thermodynamic extrinsic curvature, one may obtain a more complete geometric representation of the critical phenomena and thermodynamics. We introduce nonperturbative thermodynamic extrinsic curvature of an ideal two-dimensional gas of anyons. Using extrinsic curvature, we find new fixed points in nonperturbative thermodynamics of the anyon gas that particles behave as semions. Here, we investigate the critical behavior of thermodynamic extrinsic curvature of two-dimensional Kagome Ising model near the critical point [Formula: see text] in a constant magnetic field and show that it behaves as [Formula: see text] with [Formula: see text], where [Formula: see text] denotes the critical exponent of the specific heat. Then, we consider the three-dimensional spherical model and show that the scaling behavior is [Formula: see text], where [Formula: see text]. Finally, using a general argument, we show that extrinsic curvature [Formula: see text] has two different scaling behaviors for positive and negative [Formula: see text]. For [Formula: see text], our results indicate that [Formula: see text]. However, for [Formula: see text], we found a different scaling behavior, where [Formula: see text].

A bootstrap study of minimal model deformations

For QFTs in AdS the boundary correlation functions remain conformal even if the bulk theory has a scale. This allows one to constrain RG flows with numerical conformal bootstrap methods. We apply this idea to flows between two-dimensional CFTs, focusing on deformations of the tricritical and ordinary Ising model. We provide non-perturbative constraints for the boundary correlation functions of these flows and compare them with conformal perturbation theory in the vicinity of the fixed points. We also reproduce a completely general constraint on the sign of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T\\overline{T }$$\\end{document} deformation in two dimensions.