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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Probing strong correlations with light scattering: Example of the quantum Ising model

In this article we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap m. The Raman cross section has a strong singularity when the energy of the outgoing photon is at the spectral gap ω f ≈ m and a square root threshold when the frequency difference between the incident and outgoing photons ω i ₋ω f ≈2m. Finally, the latter feature reflects the fermionic nature of the Ising model excitations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

No unitary bootstrap for the fractal Ising model

Here, we consider the conformal bootstrap for spacetime dimension 1 < d < 2. We determine bounds on operator dimensions and compare our results with various theoretical and numerical models, in particular with resummed ϵ-expansion and Monte Carlo simulations of the Ising model on fractal lattices. The bounds clearly rule out that these models correspond to unitary conformal field theories. We also clarify the d → 1 limit of the conformal bootstrap, showing that bounds can be — and indeed are — discontinuous in this limit. This discontinuity implies that for small ϵ = d - 1 the expected critical exponents for the Ising model are disallowed, and in particular those of the d - 1 expansion. Altogether these results strongly suggest that the Ising model universality class cannot be described by a unitary CFT below d = 2. We argue this also from a bootstrap perspective, by showing that the 2 ≤ d < 4 Ising “kink” splits into two features which grow apart below d = 2.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Review of Recent Developments in the Random-Field Ising Model

A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for different probability distributions of the random fields and for diluted antiferromagnets in a field are the same. Therefore, critical universality, which is a perturbative renormalization-group prediction, holds beyond the validity regime of perturbation theory. Most notably, dimensional reduction is restored at five dimensions, i.e., the exponents of the random-field Ising model at five dimensions and those of the pure Ising ferromagnet at three dimensions are the same.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Absence of Replica Symmetry Breaking in the Transverse and Longitudinal Random Field Ising Model

It is proved that replica symmetry is not broken in the transverse and longitudinal random field Ising model. In this model, the variance of spin overlap of any component vanishes in any dimension almost everywhere in the coupling constant space in the infinite volume limit. The weak Fortuin–Kasteleyn–Ginibre property in this model and the Ghirlanda–Guerra identities in artificial models in a path integral representation based on the Lie–Trotter–Suzuki formula enable us to extend Chatterjee’s proof for the random field Ising model to the quantum model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Polychromatic Arm Exponents for the Critical Planar FK-Ising Model

Schramm–Loewner evolution (SLE) is a one-parameter family of random planar curves introduced by Schramm in 1999 as the candidates for the scaling limits of the interfaces in the planar critical lattice models. This is the only possible process with conformal invariance and a certain “domain Markov property”. In 2010, Chelkak and Smirnov proved the conformal invariance of the scaling limits of the critial planar FK-Ising model which gave the convergence of the interface to SLE{sub 16/3}. We derive the arm exponents of SLE{sub κ} for κ∈(4,8). Combining with the convergence of the interface, we derive the arm exponents of the critical FK-Ising model. We obtain six different patterns of boundary arm exponents and three different patterns of interior arm exponents of the critical planar FK-Ising model on the square lattice.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Strong-coupling expansion of multi-band interacting models: Mapping onto the transverse-field J 1 - J 2 Ising model

We investigate a class of two-dimensional two-band microscopic models in which the inter-band repulsive interactions play the dominant role. We first demonstrate three different schemes of constraining the ratios between the three types of inter-band interactions – density-density, spin exchange, and pair-hopping – that render the model free of the fermionic sign-problem for any filling and, consequently, amenable to efficient Quantum Monte Carlo simulations. We then study the behavior of these sign-problem-free models in the strong-coupling regime. In the cases where spin-rotational invariance is preserved or lowered to a planar symmetry, the strong-coupling ground state is a quantum paramagnet. However, in the case where there is only a residual Ising symmetry, the strong-coupling expansion maps onto the transverse-field J 1 - J 2 Ising model, whose pseudospins are associated with local inter-band magnetic order. We show that by varying the band structure parameters within a reasonable range of values, a variety of ground states and quantum critical points can be accessed in the strong-coupling regime, some of which are not realized in the weak-coupling regime. Here, we compare these results with the case of the single-band Hubbard model, where only intra-band repulsion is present, and whose strong-coupling behavior is captured by a simple Heisenberg model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Thermodynamic and Magnetic Properties of the Two-Dimensional Anisotropic Ising Model with Competing Interactions

The two-dimensional anisotropic Ising model with competing interactions is studied on a square lattice by Monte Carlo methods using the Wang–Landau algorithm. The temperature dependences of the main thermodynamic and magnetic parameters are calculated. The distinctive features of temperature dependences of these parameters for different values of the competing interaction are shown. The dependences of the wave number of modulated structures on the ratio of exchange interaction parameters are plotted. The phase diagram of the model is built. The coordinates of the Lifshits point and the localization region of the phases with different wave vector values are calculated by interpolating phase boundaries of the d-iagram.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Monte Carlo Study of the Effect of Initial States and Structural Defects on Nonequilibrium Critical Behavior of the Three-Dimensional Ising Model

The effect of various initial magnetizations m{sub 0} and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m{sub 0} These subclasses correspond to the system evolution from the high-temperature (m{sub 0} = 0) and low-temperature (m{sub 0} = 1) initial states with limit FDRs characteristic of these states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Analysis of the Effect of Different Initial States and Structural Defects on the Characteristics of the Nonequilibrium Critical Behavior of the 3D Ising Model

The effect of different initial values m{sub 0} of magnetization and structural defects on the nonequilibrium critical behavior of the 3D Ising model have been analyzed numerically using the Monte Carlo method. Analysis of the two-time dependences of the autocorrelation function and dynamic susceptibility has revealed a substantial influence of the initial states on the aging effects that are characterized by anomalous retardation of relaxation and correlation in the system upon an increase in the waiting time. We have studied the violations of the fluctuation–dissipation theorem and calculated the limiting fluctuation–dissipation ratio. It is shown that in the nonequilibrium critical behavior of the 3D Ising model, two universality subclasses corresponding to the evolution of the system from the high-temperature (with m{sub 0} = 0) and low-temperature (with m{sub 0} = 1) initial states with the values of the limiting fluctuation–dissipation ratio typical of these states can be singled out.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Toward a 3d Ising model with a weakly-coupled string theory dual

It has long been expected that the 3d Ising model can be thought of as a string theory, where one interprets the domain walls that separate up spins from down spins as two-dimensional string worldsheets. The usual Ising Hamiltonian measures the area of these domain walls. This theory has string coupling of unit magnitude. We add new local terms to the Ising Hamiltonian that further weight each spin configuration by a factor depending on the genus of the corresponding domain wall, resulting in a new 3d Ising model that has a tunable bare string coupling g_s g s . We use a combination of analytical and numerical methods to analyze the phase structure of this model as g_s g s is varied. We study statistical properties of the topology of worldsheets and discuss the prospects of using this new deformation at weak string coupling to find a worldsheet description of the 3d Ising transition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Quantum Ising model on (2+1)-dimensional anti–de Sitter space using tensor networks

We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using matrix product states (MPS) and matrix product operators (MPOs). We explore the bulk phase diagram of the theory on regular tessellations of hyperbolic space with coordination number seven and find disordered and ordered phases separated by a phase transition. We find that the boundary-boundary spin correlation function exhibits power law scaling deep in the disordered phase of the Ising model consistent with holography. At the critical point, we find the boundary entanglement entropy scales logarithmically with subsystem size but away from this, we see a linear scaling. In comparison, the full system exhibits a volume law scaling, which is expected in chaotic and/or highly connected systems. We also measure out of time ordered correlators (OTOCs) to explore the scrambling behavior of the theory.

Quantum spin models↗
DOE OSTI2015

AIM for Allostery: Using the Ising Model to Understand Information Processing and Transmission in Allosteric Biomolecular Systems

In performing their biological functions, molecular machines must process and transmit information with high fidelity. Information transmission requires dynamic coupling between the conformations of discrete structural components within the protein positioned far from one another on the molecular scale. This type of biomolecular “action at a distance” is termed allostery. Although allostery is ubiquitous in biological regulation and signal transduction, its treatment in theoretical models has mostly eschewed quantitative descriptions involving the system’s underlying structural components and their interactions. Here, we show how Ising models can be used to formulate an approach to allostery in a structural context of interactions between the constitutive components by building simple allosteric constructs we termed Allosteric Ising Models (AIMs). We introduce the use of AIMs in analytical and numerical calculations that relate thermodynamic descriptions of allostery to the structural context, and then show that many fundamental properties of allostery, such as the multiplicative property of parallel allosteric channels, are revealed from the analysis of such models. The power of exploring mechanistic structural models of allosteric function in more complex systems by using AIMs is demonstrated by building a model of allosteric signaling for an experimentally well-characterized asymmetric homodimer of the dopamine D2 receptor.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

The 1D Ising model and the topological phase of the Kitaev chain

It has been noted that the Kitaev chain, a p-wave superconductor with nearest-neighbor pairing amplitude equal to the hopping term Δ=t, and chemical potential μ=0, can be mapped into a nearest neighbor Ising model via a Jordan–Wigner transformation. Starting from the explicit eigenstates of the open Kitaev chain in terms of the original fermion operators, we elaborate that despite this formal equivalence the models are physically inequivalent, and show how the topological phase in the Kitaev chain maps into conventional order in the Ising model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Variational quantum simulation of the critical Ising model with symmetry averaging

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)–style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. Here, we propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.

1-dimensional spin chains↗
DOE OSTI2018

Random Crystal Field in a Mixed Spin S = 1/2 and S = 3/2 Ising Model by Renormalization Group Theory

In this work, we study the Ising model with mixed spins S = 1/2 and S = 3/2 on the hypercubic lattice and the random crystal field at the sublattice with S = 3/2 described by a two peaks law. To achieve this, we use an approximation of position space renormalization group (PSRG) namely Migdal-Kadanoff in which we use both the free energy derivative and the flow in the parameter space of the Hamiltonian. For all values of the random probability, the critical behavior is determined via the critical exponents at the second-order fixed points while at low temperatures; the discontinuities of the of the free energy derivative provide the positions of the first-order transitions. The introduction of a minimal amount of disorder causes a change in the phase diagram showing the relevance of disorder for d = 2 and d = 3. The second-order transition remains always with the same critical exponents as those of the pure model, and a new first-order transition appears at very low temperature. Also, a comparison with other similar works is given.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Paradigm for approaching the forbidden phase transition in the one-dimensional Ising model at fixed finite temperature: Single chain in a magnetic field

In a previous paper, the forbidden spontaneous phase transition in the one-dimensional Ising model was found to be approachable arbitrarily closely in decorated ladders by ultra-narrow phase crossover (UNPC) at a given finite temperature T 0 with the crossover width 2δT reduced exponentially, which resemble a genuine first-order transition with large latent heat. Here, I reveal that the forbidden phase transition can be approached at fixed T 0 as well in decorated single-chain Ising models in the presence of a magnetic field, in which T 0 is determined by the interactions involving only the decorated parts and the magnetic field, while 2δT is independently, exponentially reduced (δT = 0 means a genuine transition) by restoring the ferromagnetic interaction between the ordinary spins on the chain backbone-which was neglected in the previous studies of pseudo-transition-thus manifesting that this asymptoticity to the forbidden transition is essentially the buildup of coherence in preformed crossover of local states. Furthermore, I show that the UNPC can be realized even in the absence of the conventional geometric frustration because the magnetic field itself can induce previously unnoticed hidden spin frustration. In conclusion, these findings make the doors wide open to the engineering and utilization of UNPC as a new paradigm for exploring exotic phenomena and 1D device applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗