Showing papers on "Ising model published in 2008"

Bounding scalar operator dimensions in 4D CFT

Abstract: In an arbitrary unitary 4D CFT we consider a scalar operator phi, and the operator phi(2) defined as the lowest dimension scalar which appears in the OPE phi x phi with a nonzero coefficient. Using general considerations of OPE, conformal block decomposition, and crossing symmetry, we derive a theory-independent inequality [phi(2)] 1 we have f(d) = 2 + O(root d - 1), which shows that the free theory limit is approached continuously. We perform some checks of our bound. We find that the bound is satisfied by all weakly coupled 4D conformal fixed points that we are able to construct. The Wilson-Fischer fixed points violate the bound by a constant O( 1) factor, which must be due to the subtleties of extrapolating to 4 - epsilon dimensions. We use our method to derive an analogous bound in 2D, and check that the Minimal Models satisfy the bound, with the Ising model nearly-saturating it. Derivation of an analogous bound in 3D is currently not feasible because the explicit conformal blocks are not known in odd dimensions. We also discuss the main phenomenological motivation for studying this set of questions: constructing models of dynamical ElectroWeak Symmetry Breaking without flavor problems.

Minor-embedding in adiabatic quantum computation: I. The parameter setting problem

Abstract: We show that the NP-hard quadratic unconstrained binary optimization (QUBO) problem on a graph G can be solved using an adiabatic quantum computer that implements an Ising spin-1/2 Hamiltonian, by reduction through minor-embedding of G in the quantum hardware graph U. There are two components to this reduction: embedding and parameter setting. The embedding problem is to find a minor-embedding G emb of a graph G in U, which is a subgraph of U such that G can be obtained from G emb by contracting edges. The parameter setting problem is to determine the corresponding parameters, qubit biases and coupler strengths, of the embedded Ising Hamiltonian. In this paper, we focus on the parameter setting problem. As an example, we demonstrate the embedded Ising Hamiltonian for solving the maximum independent set (MIS) problem via adiabatic quantum computation (AQC) using an Ising spin-1/2 system. We close by discussing several related algorithmic problems that need to be investigated in order to facilitate the design of adiabatic algorithms and AQC architectures.

Ising and Spin orders in Iron-Based Superconductors

Abstract: Motivated by recent neutron scattering experiments, we study the ordering of spins in the iron-based superconductors $\mathrm{LaFeAs}({\mathrm{O}}_{1\ensuremath{-}x}{\mathrm{F}}_{x})$, assuming them in proximity to a Mott insulator in the phase diagram. The ground state of the parent system with $x=0$ is a spin-density wave with ordering wave vector $\stackrel{P\vec}{Q}=(0,\ensuremath{\pi})$ or $(\ensuremath{\pi},0)$. Upon raising the temperature, we find that the system restores SU(2) symmetry, while an Ising symmetry remains broken, explaining the experimentally observed lattice distortion to a monoclinic crystal structure. Upon further temperature increase, the spins finally disorder at a second transition. The phase transition driven by doping with charge carriers similarly splits into an $\mathrm{O}(3)$ transition and an Ising transition with $z=3$ at larger doping.

The dimension of the SLE curves

Abstract: Let γ be the curve generating a Schramm–Loewner Evolution (SLE) process, with parameter κ ≥ 0. We prove that, with probability one, the Haus-dorff dimension of γ is equal to Min(2, 1 + κ/8). Introduction. It has been conjectured by theoretical physicists that various lattice models in statistical physics (such as percolation, Potts model, Ising model, uniform spanning trees), taken at their critical point, have a continuous confor-mally invariant scaling limit when the mesh of the lattice tends to 0. Recently, Oded Schramm [15] introduced a family of random processes which he called Stochastic Loewner Evolutions (or SLE), that are the only possible conformally invariant scaling limits of random cluster interfaces (which are very closely related to all above-mentioned models). An SLE process is defined using the usual Loewner equation, where the driving function is a time-changed Brownian motion. More specifically, in the present paper we will be mainly concerned with SLE in the upper-half plane (sometimes called chordal SLE), defined by the following PDE:

Spin chirality in a molecular dysprosium triangle: the archetype of the noncollinear ising model.

Abstract: Single crystal magnetic studies combined with a theoretical analysis show that cancellation of the magnetic moments in the trinuclear Dy3+ cluster [Dy{3}(mu{3}-OH)2L3Cl(H2O){5}]Cl{3}, resulting in a nonmagnetic ground doublet, originates from the noncollinearity of the single-ion easy axes of magnetization of the Dy3+ ions that lie in the plane of the triangle at 120 degrees one from each other. This gives rise to a peculiar chiral nature of the ground nonmagnetic doublet and to slow relaxation of the magnetization with abrupt accelerations at the crossings of the discrete energy levels.

Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting Problem

Abstract: We show that the NP-hard quadratic unconstrained binary optimization (QUBO) problem on a graph $G$ can be solved using an adiabatic quantum computer that implements an Ising spin-1/2 Hamiltonian, by reduction through minor-embedding of $G$ in the quantum hardware graph $U$. There are two components to this reduction: embedding and parameter setting. The embedding problem is to find a minor-embedding $G^{emb}$ of a graph $G$ in $U$, which is a subgraph of $U$ such that $G$ can be obtained from $G^{emb}$ by contracting edges. The parameter setting problem is to determine the corresponding parameters, qubit biases and coupler strengths, of the embedded Ising Hamiltonian. In this paper, we focus on the parameter setting problem. As an example, we demonstrate the embedded Ising Hamiltonian for solving the maximum independent set (MIS) problem via adiabatic quantum computation (AQC) using an Ising spin-1/2 system. We close by discussing several related algorithmic problems that need to be investigated in order to facilitate the design of adiabatic algorithms and AQC architectures.

Spin decoherence of a heavy hole coupled to nuclear spins in a quantum dot

Abstract: We theoretically study the interaction of a heavy hole with nuclear spins in a quasi-two-dimensional III--V semiconductor quantum dot and the resulting dephasing of heavy-hole spin states. It has frequently been stated in the literature that heavy holes have a negligible interaction with nuclear spins. We show that this is not the case. In contrast, the interaction can be rather strong and will be the dominant source of decoherence in some cases. We also show that for unstrained quantum dots the form of the interaction is Ising, resulting in unique and interesting decoherence properties, which might provide a crucial advantage to using dot-confined hole spins for quantum information processing, as compared to electron spins.

Geometric frustration in buckled colloidal monolayers

Abstract: Geometric frustration arises when lattice structure prevents simultaneous minimization of local interaction energies. It leads to highly degenerate ground states and, subsequently, to complex phases of matter, such as water ice, spin ice, and frustrated magnetic materials. Here we report a simple geometrically frustrated system composed of closely packed colloidal spheres confined between parallel walls. Diameter-tunable microgel spheres are self-assembled into a buckled triangular lattice with either up or down displacements, analogous to an antiferromagnetic Ising model on a triangular lattice. Experiment and theory reveal single-particle dynamics governed by in-plane lattice distortions that partially relieve frustration and produce ground states with zigzagging stripes and subextensive entropy, rather than the more random configurations and extensive entropy of the antiferromagnetic Ising model. This tunable soft-matter system provides a means to directly visualize the dynamics of frustration, thermal excitations and defects.

Construction of Quantum Field Theories with Factorizing S-Matrices

Abstract: The subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two-dimensional Minkowski space. Employing the algebraic framework of quantum field theory, it is shown under which conditions an algebra of observables localized in a wedge-shaped region of spacetime can be used to construct model theories. A crucial input in this context is the modular nuclearity condition for wedge algebras, which implies the existence of local observables.As an application of the new method, a rigorous construction of a large family of models with factorizing S-matrices is obtained. In an inverse scattering approach, a given factorizing scattering operator is used to define certain semi-localized Wightman fields associated to it. With the help of these fields, a wedge algebra can be defined, which determines the local observable content of a well-defined quantum field theory. In this approach, the modular nuclearity condition translates to certain analyticity and boundedness conditions on the formfactors of wedge-local observables. These conditions are shown to hold for a large class of underlying S-matrices, including the scattering operators of the Sinh-Gordon model and the scaling Ising model as special examples.The so constructed models are investigated with respect to their scattering properties. They are shown to solve the inverse scattering problem for the underlying S-matrices, and a proof of asymptotic completeness for these models is given.

Ising models on locally tree-like graphs

Abstract: We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the "cavity" prediction for the limiting free energy per spin is correct for any positive temperature and external field. Further, local marginals can be approximated by iterating a set of mean field (cavity) equations. Both results are achieved by proving the local convergence of the Boltzmann distribution on the original graph to the Boltzmann distribution on the appropriate infinite random tree.

Bounding scalar operator dimensions in 4D CFT

Abstract: In an arbitrary unitary 4D CFT we consider a scalar operator \phi, and the operator \phi^2 defined as the lowest dimension scalar which appears in the OPE \phi\times\phi with a nonzero coefficient. Using general considerations of OPE, conformal block decomposition, and crossing symmetry, we derive a theory-independent inequality [\phi^2] \leq f([\phi]) for the dimensions of these two operators. The function f(d) entering this bound is computed numerically. For d->1 we have f(d)=2+O(\sqrt{d-1}), which shows that the free theory limit is approached continuously. We perform some checks of our bound. We find that the bound is satisfied by all weakly coupled 4D conformal fixed points that we are able to construct. The Wilson-Fischer fixed points violate the bound by a constant O(1) factor, which must be due to the subtleties of extrapolating to 4-\epsilon dimensions. We use our method to derive an analogous bound in 2D, and check that the Minimal Models satisfy the bound, with the Ising model nearly-saturating it. Derivation of an analogous bound in 3D is currently not feasible because the explicit conformal blocks are not known in odd dimensions. We also discuss the main phenomenological motivation for studying this set of questions: constructing models of dynamical ElectroWeak Symmetry Breaking without flavor problems.

Phase diagram and entanglement of the Ising model with Dzyaloshinskii-Moriya interaction

Abstract: We have studied the phase diagram and entanglement of the one-dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization-group (QRG) approach to get the stable fixed points, critical point, and the scaling of coupling constants. This model has two phases: antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite-size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of spin operators which are defined by a nonlocal transformation.

Ground state fidelity from tensor network representations

Abstract: For any D-dimensional quantum lattice system, the fidelity between two ground state many-body wave functions is mapped onto the partition function of a D-dimensional classical statistical vertex lattice model with the same lattice geometry. The fidelity per lattice site, analogous to the free energy per site, is well defined in the thermodynamic limit and can be used to characterize the phase diagram of the model. We explain how to compute the fidelity per site in the context of tensor network algorithms, and demonstrate the approach by analyzing the two-dimensional quantum Ising model with transverse and parallel magnetic fields.

Discrete complex analysis on isoradial graphs

Abstract: We study discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones. Along with discrete analogues of several classical results, we prove uniform convergence of discrete harmonic measures, Green's functions and Poisson kernels to their continuous counterparts. Among other applications, the results can be used to establish universality of the critical Ising and other lattice models.

Social applications of two-dimensional Ising models

Abstract: I review three socio-economic models of economic opinions, urban segregation, and language change and show that the well-known two-dimensional Ising model gives about the same results in each case.

Fractional magnetization plateaus and magnetic order in the Shastry-Sutherland magnet TmB4.

Abstract: We investigate the phase diagram of ${\mathrm{TmB}}_{4}$, an Ising magnet on a frustrated Shastry-Sutherland lattice, by neutron diffraction and magnetization experiments. At low temperature we find N\'eel order at low field, ferrimagnetic order at high field, and an intermediate phase with magnetization plateaus at fractional values $M/{M}_{\mathrm{sat}}=1/7,1/8,1/9,\dots{}$ and spatial stripe structures. Using an effective $S=1/2$ model and its equivalent two-dimensional fermion gas we suggest that the magnetic properties of ${\mathrm{TmB}}_{4}$ are related to the fractional quantum Hall effect of a 2D electron gas.

Giant magnetocaloric effect in the Ising antiferromagnet DySb

Abstract: The magnetic phase transitions and the magnetocaloric effect in the Ising antiferromagnet DySb have been studied. A field-induced sign change of the magnetocaloric effect has been observed which is related to a first-order field-induced metamagnetic transition from the antiferromagnetic to the ferromagnetic states at/below the Neel temperature TN, while the negative field-induced entropy change is found to be associated with the first-order magnetic transition from the paramagnetic to the ferromagnetic states above TN. The large magnetic-entropy change (−20.6J∕kgK at 11K for a field change of 7T), together with small hysteresis, suggests that DySb could be a potential material for magnetic refrigeration in the low-temperature range.

Optimal nonlinear passage through a quantum critical point.

Abstract: We analyze the problem of optimal adiabatic passage through a quantum critical point. We show that to minimize the number of defects the tuning parameter should be changed as a power law in time. The optimal power is proportional to the logarithm of the total passage time multiplied by universal critical exponents characterizing the phase transition. We support our results by the general scaling analysis and by explicit calculations for the transverse-field Ising model.

The Wulff Crystal in Ising and Percolation Models

Abstract: Phase coexistence and subadditivity.- Presentation of the models.- Ising model.- Bernoulli percolation.- FK or random cluster model.- Main results.- The Wulff crystal.- Large deviation principles.- Large deviation theory.- Surface large deviation principles.- Volume large deviations.- Fundamental probabilistic estimates.- Coarse graining.- Decoupling.- Surface tension.- Interface estimate.- Basic geometric tools.- Sets of finite perimeter.- Surface energy.- The Wulff theorem.- Final steps of the proofs.- LDP for the cluster shapes.- Enhanced upper bound.- LDP for FK percolation.- LDP for Ising.

Principle of isomorphism and complete scaling for binary-fluid criticality.

Abstract: The extension of the principle of critical-point universality to binary fluid mixtures, known as isomorphism of critical phenomena, has been reformulated in terms of complete scaling, a concept that properly matches asymmetric fluid-phase behavior with the symmetric Ising model. The controversial issue of the proper definition of the order parameter in binary fluid mixtures is clarified. We show that asymmetry of liquid-liquid coexistence in terms of mole fractions originates from two different sources: one is associated with a correlation between concentration and entropy fluctuations, whereas the other source is the correlation between concentration and density fluctuations. By analyzing the coexistence curves of liquid solutions of nitrobenzene in a series of hydrocarbons (from n -pentane to n -hexadecane), we have separated these two sources of asymmetry and found that the leading nonanalytical contribution to the asymmetry correlates linearly with the solute-solvent molecular-volume ratio. Other thermodynamic consequences of complete scaling for binary mixtures, such as an analog of the Yang-Yang anomaly in the behavior of the heat capacity and a curvature correction to the interfacial tension, are also discussed.

NOTE ON THE E. ISING'S PAPER ,,BEITRAG ZUR THEORIE DES FERROMAGNETISMUS" (Zs. Physik, 31, 253 (1925))

Abstract: In this brief note some inaccuracy which occured in wellknown paper by E. Ising [1] is discussed.

Faster solutions of the inverse pairwise Ising problem

Abstract: Princeton Center for Theoretical Physics, Princeton University, Princeton, NJ 08544(Dated: February 4, 2008)Recent work has shown that probabilistic models based on pairwise interactions|in the simplestcase, the Ising model|provide surprisingly accurate descriptions of experiments on real biologicalnetworks ranging from neurons to genes. Finding these models requires us to solve an inverse prob-lem: given experimentally measured expectation values, what are the parameters of the underlyingHamiltonian? This problem sits at the intersection of statistical physics and machine learning, andwe suggest that more ecient solutions are possible by merging ideas from the two elds. We usea combination of recent coordinate descent algorithms with an adaptation of the histogram MonteCarlo method, and implement these techniques to take advantage of the sparseness found in data onreal neurons. The resulting algorithm learns the parameters of an Ising model describing a networkof forty neurons within a few minutes. This opens the possibility of analyzing much larger data setsnow emerging, and thus testing hypotheses about the collective behaviors of these networks.I. INTRODUCTION

Multiscale entanglement renormalization ansatz in two dimensions: quantum Ising model.

Abstract: We propose a symmetric version of the multiscale entanglement renormalization ansatz in two spatial dimensions (2D) and use this ansatz to find an unknown ground state of a 2D quantum system. Results in the simple 2D quantum Ising model on the $8\ifmmode\times\else\texttimes\fi{}8$ square lattice are found to be very accurate even with the smallest nontrivial truncation parameter.

The mean field ising model trough interpolating techniques

Abstract: Aim of this paper is to illustrate how some recent techniques developed within the framework of spin glasses do work on simpler model, focusing on the method and not on the analyzed system. To fulfill our will the candidate model turns out to be the paradigmatic mean field Ising model. The model is introduced and investigated with the interpolation techniques. We show the existence of the thermodynamic limit, bounds for the free energy density, the explicit expression for the free energy with its suitable expansion via the order parameter, the self-consistency relation, the phase transition, the critical behavior and the self-averaging properties. At the end a formulation of a Parisi-like theory is tried and discussed.

Exact relationship between the entanglement entropies of XY and quantum Ising chains

Abstract: We consider two prototypical quantum models, the spin-1/2 XY chain and the quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of l spins in homogeneous or inhomogeneous systems of length L. By using two different approaches, free-fermion techniques and perturbational expansion, an exact relationship between the entropies is revealed. Using this relation we translate known results between the two models and obtain, among others, the additive constant of the entropy of the critical homogeneous quantum Ising chain and the effective central charge of the random XY chain.

Non-Perturbative Renormalization

Abstract: Renormalization Mathematical Techniques QED2, Thirring and Gross-Neveu Models Ward Identities Chiral Anomalies and the Adler-Bardeen Theorem Vanishing of Beta Function Wilson Fermion and Axiom Verification Infrared QED4 Universality in Ising Models Nonuniversality in Vertex or Askin-Teller Models The Anisotropic Ashkin-Teller Model Luttinger Liquids and Spin Chains The 1D Hubbard Model Fermi Liquid Behavior in the 2D Hubbard Model The BCS Model

Entanglement evolution after connecting finite to infinite quantum chains

Abstract: We study zero-temperature XX chains and transverse Ising chains and join an initially separate finite piece on one or on both sides to an infinite remainder. In both critical and non-critical systems we find a typical increase of the entanglement entropy after the quench, followed by a slow decay towards the value of the homogeneous chain. In the critical case, the predictions of conformal field theory are verified for the first phase of the evolution, while at late times a step structure can be observed.

Critical behavior of three-dimensional Ising spin glass models

Abstract: We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin glass models on cubic lattices of size $L$: the $\ifmmode\pm\else\textpm\fi{}J$ (Edwards-Anderson) Ising model for two values of the disorder parameter $p$, $p=0.5$ and $p=0.7$ (up to $L=28$ and $L=20$, respectively), and the bond-diluted bimodal model for bond-occupation probability ${p}_{b}=0.45$ (up to $L=16$). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent $\ensuremath{\omega}$ related to the leading irrelevant operator: $\ensuremath{\omega}=1.0(1)$. Shorter Monte Carlo simulations of the bond-diluted bimodal models at ${p}_{b}=0.7$ and ${p}_{b}=0.35$ (up to $L=10$) and of the Ising spin glass model with Gaussian bond distribution (up to $L=8$) also support the existence of a unique Ising spin glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents. We obtain $\ensuremath{ u}=2.45(15)$ and $\ensuremath{\eta}=\ensuremath{-}0.375(10)$.