Showing papers on "Ising model published in 2011"

Strong axiality and Ising exchange interaction suppress zero-field tunneling of magnetization of an asymmetric Dy2 single-molecule magnet.

Abstract: The high axiality and Ising exchange interaction efficiently suppress quantum tunneling of magnetization of an asymmetric dinuclear Dy(III) complex, as revealed by combined experimental and theoretical investigations. Two distinct regimes of blockage of magnetization, one originating from the blockage at individual Dy sites and the other due to the exchange interaction between the sites, are separated for the first time. The latter contribution is found to be crucial, allowing an increase of the relaxation time by 3 orders of magnitude.

Mapping of Ising models onto injection-locked laser systems

Abstract: We propose a mapping protocol to implement Ising models in injection-locked laser systems. The proposed scheme is based on optical coherent feedback and can be potentially applied for large-scale Ising problems.

Two-Stage Ordering of Spins in Dipolar Spin Ice on the Kagome Lattice

Abstract: Spin ice, a peculiar thermal state of a frustrated ferromagnet on the pyrochlore lattice, has a finite entropy density and excitations carrying magnetic charge. By combining analytical arguments and Monte Carlo simulations, we show that spin ice on the two-dimensional kagome lattice orders in two stages. The intermediate phase has ordered magnetic charges and is separated from the paramagnetic phase by an Ising transition. The transition to the low-temperature phase is of the three-state Potts or Kosterlitz-Thouless type, depending on the presence of defects in the charge order.

In-plane electronic anisotropy of underdoped '122' Fe-arsenide superconductors revealed by measurements of detwinned single crystals

Abstract: The parent phases of the Fe-arsenide superconductors harbor an antiferromagnetic ground state. Significantly, the Neel transition is either preceded or accompanied by a structural transition that breaks the four-fold symmetry of the high-temperature lattice. Borrowing language from the field of soft condensed matter physics, this broken discrete rotational symmetry is widely referred to as an Ising nematic phase transition. Understanding the origin of this effect is a key component of a complete theoretical description of the occurrence of superconductivity in this family of compounds, motivating both theoretical and experimental investigation of the nematic transition and the associated in-plane anisotropy. Here we review recent experimental progress in determining the intrinsic in-plane electronic anisotropy as revealed by resistivity, reflectivity and angle-resolved photoemission spectroscopy measurements of detwinned single crystals of underdoped Fe-arsenide superconductors in the '122' family of compounds.

Adaptive cluster expansion for inferring boltzmann machines with noisy data.

Abstract: We introduce a procedure to infer the interactions among a set of binary variables, based on their sampled frequencies and pairwise correlations. The algorithm builds the clusters of variables contributing most to the entropy of the inferred Ising model and rejects the small contributions due to the sampling noise. Our procedure successfully recovers benchmark Ising models even at criticality and in the low temperature phase, and is applied to neurobiological data.

Entanglement entropy from charge statistics: Exact relations for noninteracting many-body systems

Abstract: We present an exact expression for the entanglement entropy generated at a quantum point contact between noninteracting electronic leads in terms of the full counting statistics of charge fluctuations, which we illustrate with examples from both equilibrium and nonequilibrium transport The formula is also applicable to ground-state entanglement entropy in systems described by noninteracting fermions in any dimension, which in one dimension include the critical spin-1/2 $\mathit{XX}$ and Ising models where conformal field theory predictions for the entanglement entropy are reproduced from the full counting statistics These results may play an important role in experimental measurements of entanglement entropy in mesoscopic structures and cold atoms in optical lattices

Magnetic properties of a cylindrical Ising nanowire (or nanotube)

Abstract: Magnetic properties (phase diagram and magnetization) of a cylindrical Ising nanowire or nanotube are investigated by the use of the effective-field theory with correlations. Particular emphasis is given to the effects of the surface and its dilution on them. Much attention is paid to the thermal variation of the magnetization when the spins at the surface are coupled antiferromagnetically to the ferromagnetic core spins by the negative shell coupling. The effects of dilution at the surface, the surface exchange interaction, and the shell coupling on the magnetization profiles are investigated. We find a number of characteristic phenomena for them.

In-plane electronic anisotropy of underdoped "122" Fe-arsenide superconductors revealed by measurements of detwinned single crystals

Abstract: The parent phases of the Fe-arsenide superconductors harbor an antiferromagnetic ground state. Significantly, the N\'eel transition is either preceded or accompanied by a structural transition that breaks the four fold symmetry of the high-temperature lattice. Borrowing language from the field of soft condensed matter physics, this broken discrete rotational symmetry is widely referred to as an Ising nematic phase transition. Understanding the origin of this effect is a key component of a complete theoretical description of the occurrence of superconductivity in this family of compounds, motivating both theoretical and experimental investigation of the nematic transition and the associated in-plane anisotropy. Here we review recent experimental progress in determining the intrinsic in-plane electronic anisotropy as revealed by resistivity, reflectivity and ARPES measurements of detwinned single crystals of underdoped Fe arsenide superconductors in the "122" family of compounds.

Second-Order Phase Transition in Causal Dynamical Triangulations

Abstract: Causal dynamical triangulations are a concrete attempt to define a nonperturbative path integral for quantum gravity. We present strong evidence that the lattice theory has a second-order phase transition line, which can potentially be used to define a continuum limit in the conventional sense of nongravitational lattice theories.

Magnetic relaxation of single-molecule magnets in an external magnetic field: an ising dimer of a terbium(III)-phthalocyaninate triple-decker complex.

Abstract: The idea of using a single spin as a “bit” of information to prepare high-density storage and quantum-computing deACHTUNGTRENNUNGvices has caused an increase in scientific and technological interests. Quantum tunneling of the magnetization (QTM) in double-well potentials, which is a characteristic property of single-molecule magnets (SMMs), is the underlying phenomenon for this idea. On the basis of the properties of lanthanoid–phthalocyaninate ([LnPc2]) SMMs, [4] we believe that [TbPc2] can be used as a “bit” of information in highdensity storage technology by taking advantage of the single up-spin/down-spin property, which is equivalent to 2. The up-spin/down-spin properties of tripleand quadrupledecker-type SMMs are equivalent to 2 and 2, respectively, in relation to the number of spins. We have recently reported the characteristics of [MPc2] and [MPc] (M= Tb, Dy, and Y) deposited on an AuACHTUNGTRENNUNG(111) surface in an ultrahigh vacuum (UHV) using a dry process technique. Both [MPc2] and [MPc] are present on the AuACHTUNGTRENNUNG(111) surface on the basis of height profiles and dI/dV mapping obtained by using scanning tunneling microscopy (STM) and spectroscopy (STS). A Kondo peak, which is due to coupling between magnetic impurities, including Tb ions, and conduction electrons from the STS, is only observed at the center of [TbPc] at a Kondo temperature (TK) of 250 K. More recently, we have observed a Kondo peak for [TbPc2] on an AuACHTUNGTRENNUNG(111) surface. Therefore, the relation between TK and the blocking temperature (TB) must be discussed further. In addition, the properties of SMMs and the Kondo effect can be modulated with an external magnetic field. Here we present the results of studies on the SMM properties of a new Tb triple-decker phthalocyaninate derivative, [Tb2ACHTUNGTRENNUNG(obPc)3] (1; obPc =dianion of 2,3,9,10,16,17,23,24octabutoxyphthalocyanine). The relationships among the molecular structure, ligand-field, ground-state, and SMM properties in a direct current (dc) magnetic field are discussed. It is important to both understand and control the quantum properties of SMMs with an external field. The triple-decker complex 1 is composed of three Pc ligACHTUNGTRENNUNGands and two Tb ions, resulting in a neutral complex with a closed shell p electron system. We used a Pc ligand with 2,3,9,10,16,17,23,24-octabutoxy substituents because it should have a higher solubility and crystallization should be easier. Complex 1 was synthesized in one step starting from [Tb ACHTUNGTRENNUNG(acac)3]·4H2O and H2obPc, following a published procedure (see Experimental Section). This complex is soluble in most organic solvents, except for alcohols. Complex 1 crystallized with ethanol in the crystal lattice in the triclinic space group P1̄, as shown in Figure 1. The crystal data are summarized in Table S1 and crystal-packing [a] Dr. K. Katoh, Prof. B. K. Breedlove, Prof. M. Yamashita Department of Chemistry, Graduate School of Science Tohoku University, 6–3 Aramaki-Aza-Aoba, Aoba-ku Sendai, Miyagi 980-8578 (Japan) Fax: (+81) 22-795-6548 E-mail : kkatoh@m.tains.tohoku.ac.jp yamasita@agnus.chem.tohoku.ac.jp [b] Prof. T. Kajiwara Department of Chemistry, Faculty of Science Nara Women s University, Nishi-Machi Kita-Uoya, Nara 565-0871 (Japan) [c] Prof. M. Nakano Department of Applied Chemistry Graduate School of Engineering, 2–1 Yamadaoka Suita, Osaka 565-0871 (Japan) [d] Prof. Y. Nakazawa, Prof. N. Ishikawa Department of Chemistry, Graduate School of Science 1-1 Machikaneyama-Cho, Toyonaka Osaka 560-0043 (Japan) [e] Prof. W. Wernsdorfer Laboratory Louis N el, CNRS, BP 166, 38042 Grenoble Cedex 9 (France) Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201002026.

Dynamical transitions and quantum quenches in mean-field models

Abstract: We develop a generic method to compute the dynamics induced by quenches in completely connected quantum systems. These models are expected to provide a mean-field description at least of the short-time dynamics of finite-dimensional systems. We apply our method to the Bose–Hubbard model, to a generalized Jaynes–Cummings model, and to the Ising model in a transverse field. We find that the quantum evolution can be mapped onto a classical effective dynamics, which involves only a few intensive observables. For some special parameters of the quench, peculiar dynamical transitions occur. They result from singularities of the classical effective dynamics and are reminiscent of the transition recently found in the fermionic Hubbard model. Finally, we discuss the generality of our results and possible extensions.

Connection Probabilities and RSW-type Bounds for the Two-Dimensional FK Ising Model

Abstract: We prove Russo-Seymour-Welsh-type uniform bounds on crossing probabilities for the FK Ising (FK percolation with cluster weight q = 2) model at criticality, independent of the boundary conditions. Our proof relies mainly on Smirnov's fermionic observable for the FK Ising model [24], which allows us to get precise estimates on boundary connection probabilities. We stay in a discrete setting; in particular, we do not make use of any continuum limit, and our result can be used to derive directly several noteworthy properties—including some new ones—among which are the fact that there is no infinite cluster at criticality, tightness properties for the interfaces, and the existence of several critical exponents, in particular the half-plane, one-arm exponent. Such crossing bounds are also instrumental for important applications such as constructing the scaling limit of the Ising spin field [6] and deriving polynomial bounds for the mixing time of the Glauber dynamics at criticality [17]

Thermal quantum and classical correlations and entanglement in the XY spin model with three-spin interaction

Abstract: Pairwise quantum discord (QD) and classical correlation (CC) are studied in the $\mathit{XY}$ spin chain with three-spin interaction. We analyze their capability in detecting quantum phase transitions (QPTs) at both zero and finite temperatures and find that the pairwise QD of two neighboring spins is more reliable than that of any other distances in identifying QPTs. Both the QD and CC detect quantum critical points associated with first- and higher-order QPTs caused by field and three-spin interactions at finite temperatures. In addition, we find a different finite-size scaling behavior for QD from previous reports for the transverse field Ising case and show some interesting phenomena of QD and entanglement of formation for finite temperatures.

Ising exponents from the functional renormalisation group

Abstract: We study the 3d Ising universality class using the functional renormalization group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and antisymmetric corrections to scaling, the anomalous dimension, the scaling solution, and the eigenperturbations at criticality. We also study the cross correlations of scaling exponents, their dependence on dimensionality, and the numerical convergence of the derivative expansion. Collecting all available data from functional renormalization group studies to date, we estimate that systematic errors are in good agreement with findings from Monte Carlo simulations, ϵ-expansion techniques, and resummed perturbation theory.

Semiclassical theory for quantum quenches in finite transverse Ising chains

Abstract: We present a quantitative semiclassical theory for the nonequilibrium dynamics of transverse Ising chains after quantum quenches, in particular, sudden changes of the transverse field strength. We obtain accurate predictions for the quench-dependent relaxation times and correlation lengths, and also about the recurrence times and quasiperiodicity of time-dependent correlations in finite systems with open or periodic boundary conditions. We compare the quantitative predictions of our semiclassical theory (local magnetization, equal-time bulk-bulk and surface-to-bulk correlations, and bulk autocorrelations) with the results from exact free-fermion calculations, and discuss the range of applicability of the semiclassical theory and possible generalizations and extensions.

Plasma analogy and non-Abelian statistics for Ising-type quantum Hall states

Abstract: We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction $\ensuremath{ u}=5/2$. We complete the program started in V. Gurarie and C. Nayak, [Nucl. Phys. B 506, 685 (1997)]. and show that the degenerate four-quasihole and six-quasihole wave functions of the Moore-Read Pfaffian state are orthogonal with equal constant norms in the basis given by conformal blocks in a $c=1+\frac{1}{2}$ conformal field theory. As a consequence, this proves that the non-Abelian statistics of the excitations in this state are given by the explicit analytic continuation of these wave functions. Our proof is based on a plasma analogy derived from the Coulomb gas construction of Ising model correlation functions involving both order and (at most two) disorder operators. We show how this computation also determines the non-Abelian statistics of collections of more than six quasiholes and give an explicit expression for the corresponding conformal block-derived wave functions for an arbitrary number of quasiholes. Our method also applies to the anti-Pfaffian wave function and to Bonderson-Slingerland hierarchy states constructed over the Moore-Read and anti-Pfaffian states.

Robustness of a Perturbed Topological Phase

Abstract: We investigate the stability of the topological phase of the toric code model in the presence of a uniform magnetic field by means of variational and high-order series expansion approaches. We find that when this perturbation is strong enough, the system undergoes a topological phase transition whose first- or second-order nature depends on the field orientation. When this transition is of second order, it is in the Ising universality class except for a special line on which the critical exponent driving the closure of the gap varies continuously, unveiling a new topological universality class.

Exact bosonization of the Ising model

Abstract: We present exact combinatorial versions of bosonization identities, which equate the product of two Ising correlators with a free field (bosonic) correlator. The role of the discrete free field is played by the height function of an associated bipartite dimer model. Some applications to the asymptotic analysis of Ising correlators are discussed.

Statistical mechanics of the Cluster-Ising model

Abstract: We study a Hamiltonian system describing a three-spin-$1/2$ clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.

Anomalies in the entanglement properties of the square-lattice Heisenberg model

Abstract: We compute the bipartite entanglement properties of the spin-half square-lattice Heisenberg model by a variety of numerical techniques that include valence-bond quantum Monte Carlo (QMC), stochastic series expansion QMC, high-temperature series expansions, and zero-temperature coupling constant expansions around the Ising limit. We find that the area law is always satisfied, but in addition to the entanglement entropy per unit boundary length, there are other terms that depend logarithmically on the subregion size, arising from broken symmetry in the bulk and from the existence of corners at the boundary. We find that the numerical results are anomalous in several ways. First, the bulk term arising from broken symmetry deviates from an exact calculation that can be done for a mean-field N\'eel state. Second, the corner logs do not agree with the known results for noninteracting Boson modes. And, third, even the finite-temperature mutual information shows an anomalous behavior as $T$ goes to zero, suggesting that the $T\ensuremath{\rightarrow}0$ and $L\ensuremath{\rightarrow}\ensuremath{\infty}$ limits do not commute. These calculations show that entanglement entropy demonstrates a very rich behavior in $dg1$, which deserves further attention.

Two-dimensional Ising-like model with specific edge effects for spin-crossover nanoparticles: A Monte Carlo study

Abstract: We analyzed the size effect of spin-crossover transition nanoparticles in a two-dimensional core-shell model, where the edge atoms are constrained to the high-spin (HS) state. Using Monte Carlo (MC) simulations, we showed that this specific edge effect lowers the equilibrium temperature and enhances the HS residual at low temperature; these results are in very good agreement with recent experimental data. Within a very simple working assumption, we obtained an analytical expression for the size dependence of the equilibrium temperature that is in excellent agreement with the MC results. The model leads to a nontrivial size dependence of the hysteresis width, which is similar to a---size-dependent---negative pressure effect induced by the HS edges. To reach the best agreement with experimental data, we accounted for the size distribution of the experimental samples.

Tailoring Three-Point Functions and Integrability III. Classical Tunneling

Abstract: We compute three-point functions between one large classical operator and two large BPS operators at weak coupling. We consider operators made out of the scalars of N=4 SYM, dual to strings moving in the sphere. The three-point function exponentiates and can be thought of as a classical tunneling process in which the classical string-like operator decays into two classical BPS states. From an Integrability/Condensed Matter point of view, we simplified inner products of spin chain Bethe states in a classical limit corresponding to long wavelength excitations above the ferromagnetic vacuum. As a by-product we solved a new long-range Ising model in the thermodynamic limit.

High-dimensional structure estimation in Ising models: Local separation criterion

Abstract: We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the presence of sparse local separators between node pairs in the underlying graph. For such graphs, the proposed algorithm has a sample complexity of $n=\Omega(J_{\min}^{-2}\log p)$, where $p$ is the number of variables, and $J_{\min}$ is the minimum (absolute) edge potential in the model. We also establish nonasymptotic necessary and sufficient conditions for structure estimation.

Quantum zigzag transition in ion chains.

Abstract: A string of trapped ions at zero temperature exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrational modes. We argue that this is a quantum phase transition, which can be experimentally realized and probed. Indeed, by means of a mapping to the Ising model in a transverse field, we estimate the quantum critical point in terms of the system parameters, and find a finite, measurable deviation from the critical point predicted by the classical theory. A measurement procedure is suggested which can probe the effects of quantum fluctuations at criticality. These results can be extended to describe the transverse instability of ultracold polar molecules in a one-dimensional optical lattice.

Infinite-disorder scaling of random quantum magnets in three and higher dimensions

Abstract: Using a very efficient numerical algorithm of the strong disorder renormalization group method we have extended the investigations about the critical behavior of the random transverse-field Ising model in three and four dimensions, as well as for Erd\H os-Renyi random graphs, which represent infinite dimensional lattices. In all studied cases an infinite disorder quantum critical point is identified, which ensures that the applied method is asymptotically correct and the calculated critical exponents tend to the exact values for large scales. We have found that the critical exponents are independent of the form of (ferromagnetic) disorder and they vary smoothly with the dimensionality.

Quantum Quenches in the Hubbard Model: Time Dependent Mean Field Theory and The Role of Quantum Fluctuations

Abstract: We study the nonequilibrium dynamics in the fermionic Hubbard model after a sudden change of the interaction strength. To this scope, we introduce a time-dependent variational approach in the spirit of the Gutzwiller ansatz. At the saddle-point approximation, we find at half filling a sharp transition between two different regimes of small and large coherent oscillations, separated by a critical line of quenches where the system is found to relax. Any finite doping washes out the transition, leaving aside just a sharp crossover. In order to investigate the role of quantum fluctuations, we map the model onto an auxiliary quantum Ising model in a transverse field coupled to free fermionic quasiparticles. Remarkably, the Gutzwiller approximation turns out to correspond to the mean-field decoupling of this model in the limit of infinite coordination lattices. The advantage is that we can go beyond mean field and include Gaussian fluctuations around the non-equilibrium mean-field dynamics. Unlike at equilibrium, we find that quantum fluctuations become massless and eventually unstable before the mean-field dynamical critical line, which suggests they could even alter qualitatively the mean-field scenario.

Compensation temperature in a cylindrical Ising nanowire (or nanotube)

Abstract: The critical temperature and the compensation temperature in a cylindrical Ising nanowire (or nanotube) with a negative interlayer coupling at the surface are investigated by the use of both the effective-field theory with correlations and the shell-core concept. Particular emphasis is given to the effects of the surface and its dilution on them. We have found that, for appropriate values of the system parameters, a compensation point may be obtained in the present systems.

The Bethe approximation for solving the inverse Ising problem: a comparison with other inference methods

Abstract: The inverse Ising problem consists in inferring the coupling constants of an Ising model given the correlation matrix. The fastest methods for solving this problem are based on mean-field approximations, but which one performs better in the general case is still not completely clear. In the first part of this work, I summarize the formulas for several mean- field approximations and I derive new analytical expressions for the Bethe approximation, which allow to solve the inverse Ising problem without running the Susceptibility Propagation algorithm (thus avoiding the lack of convergence). In the second part, I compare the accuracy of different mean field approximations on several models (diluted ferromagnets and spin glasses) defined on random graphs and regular lattices, showing which one is in general more effective. A simple improvement over these approximations is proposed. Also a fundamental limitation is found in using methods based on TAP and Bethe approximations in presence of an external field.

Logarithmic Terms in Entanglement Entropies of 2D Quantum Critical Points and Shannon Entropies of Spin Chains

Abstract: Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the ``Shannon entropy'' of a 1D spin chain with open boundary conditions. The Shannon entropy of the $XXZ$ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient $\ifmmode\pm\else\textpm\fi{}0.25$. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or R\'enyi index resulting from flows to different boundary conditions at the entanglement cut.