Simple Spin Model Research Articles

The melting of stable glasses is governed by nucleation-and-growth dynamics.

We discuss the microscopic mechanisms by which low-temperature amorphous states, such as ultrastable glasses, transform into equilibrium fluids, after a sudden temperature increase. Experiments suggest that this process is similar to the melting of crystals, thus differing from the behaviour found in ordinary glasses. We rationalize these observations using the physical idea that the transformation process takes place close to a "hidden" equilibrium first-order phase transition, which is observed in systems of coupled replicas. We illustrate our views using simulation results for a simple two-dimensional plaquette spin model, which is known to exhibit a range of glassy behaviour. Our results suggest that nucleation-and-growth dynamics, as found near ordinary first-order transitions, is also the correct theoretical framework to analyse the melting of ultrastable glasses. Our approach provides a unified understanding of multiple experimental observations, such as propagating melting fronts, large kinetic stability ratios, and "giant" dynamic length scales. We also provide a comprehensive discussion of available theoretical pictures proposed in the context of ultrastable glass melting.

Leggett-Garg inequalities and no-signaling in time: A quasiprobability approach

The Leggett-Garg (LG) inequalities were proposed in order to assess whether sets of pairs of sequential measurements on a single quantum system can be consistent with an underlying notion of macrorealism. Here, the LG inequalities are explored using a simple quasi-probability linear in the projection operators to describe the properties of the system at two times. We show that this quasi-probability is measurable, has the same correlation function as the usual two-time measurement probability (for the bivalent variables considered here) and has the key property that the probabilities for the later time are independent of whether an earlier measurement was made, a generalization of the no-signalling in time condition of Kofler and Brukner. We argue that this quasi-probability, appropriately measured, provides a non-invasive measure of macrorealism per se at the two time level. This measure, when combined with the LG inequalities, provides a characterization of macrorealism more detailed than that provided by the LG inequalities alone. When the quasi-probability is non-negative, the LG system has a natural parallel with the EPRB system and Fine's theorem. A simple spin model illustrating key features of the approach is exhibited.

Large N matrices from a nonlocal spin system

Large N matrices underpin the best understood models of emergent spacetime. We suggest that large N matrices can themselves be emergent from simple quantum mechanical spin models with finite dimensional Hilbert spaces. We exhibit the emergence of large N matrices in a nonlocal statistical physics model of order N2 Ising spins. The spin partition function is shown to admit a large N saddle described by a matrix integral, which we solve. The matrix saddle is dominant at high temperatures, metastable at intermediate temperatures and ceases to exist below a critical order one temperature. The matrix saddle is disordered in a sense we make precise and competes with ordered low energy states. We verify our analytic results by Monte Carlo simulation of the spin system.

Tunable magnetic helicity in Mn1−xFexGe: A Monte Carlo simulation

Motivated by recent experiments on B20 compound Mn1−xFexGe, we explore the variations of spin structures and magnetic helicity γm in Mn1−xFexGe as a function of concentration x, using Monte Carlo simulation. We propose a simple spin model including hybrid Dzyaloshinskii-Moriya (DM) interactions with different signs in FeGe and MnGe. The results reveal a series of spin structures with helicity γm varying continuously from negative values to positive values upon decreasing x (0.0 ≤ x ≤ 1.0). The simulated x-dependence of the spin structures is consistent with experimental observations, suggesting the validity of the present hybrid model. This study sheds light on control of magnetic helicity in helimagnets, by mixing crystals with different DM interactions.

Z3symmetry-protected topological phases in the SU(3) AKLT model

We study $\mathbb{Z}_3$ symmetry-protected topological (SPT) phases in one-dimensional spin systems with $Z_3 \times Z_3$ symmetry. We construct ground-state wave functions of the matrix product form for nontrivial $\mathbb{Z}_3$ phases and their parent Hamiltonian from a cocycle of the group cohomology $H^2(Z_3\times Z_3,U(1))$. The Hamiltonian is an SU(3) version of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, consisting of bilinear and biquadratic terms of su(3) generators in the adjoint representation. A generalization to the SU($N$) case, the SU($N$) AKLT Hamiltonian, is also presented which realizes nontrivial $\mathbb{Z}_N$ SPT phases. We use the infinite-size variant of the density matrix renormalization group (iDMRG) method to determine the ground-state phase diagram of the SU(3) bilinear-biquadratic model as a function of the parameter $\theta$ controlling the ratio of the bilinear and biquadratic coupling constants. The nontrivial $\mathbb{Z}_3$ SPT phase is found for a range of the parameter $\theta$ including the point of vanishing biquadratic term ($\theta=0$) as well as the SU(3) AKLT point [$\theta=\arctan(2/9)$]. A continuous phase transition to the SU(3) dimer phase takes place at $\theta \approx -0.027\pi$, with a central charge $c\approx3.2$. For SU(3) symmetric cases we define string order parameters for the $\mathbb{Z}_3$ SPT phases in a similar way to the conventional Haldane phase. We propose simple spin models that effectively realize the SU(3) and SU(4) AKLT models.

A simple spin model for three step relaxation and secondary processes in glass formers

A number of general trends are known to occur in systems displaying secondary processes in glasses and glass formers. Universal features can be identified as components of large and small cooperativeness whose competition leads to excess wings or apart peaks in the susceptibility spectrum. To the aim of understanding such rich and complex phenomenology we analyze the behavior of a model combining two apart glassy components with a tunable different cooperativeness. The model salient feature is, indeed, based on the competition of the energetic contribution of groups of dynamically relevant variables, e.g., density fluctuations, interacting in small and large sets. We investigate how the model is able to reproduce the secondary processes physics without further ad hoc ingredients, displaying known trends and properties under cooling or pressing.

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Using a methodology based on noncollinear coupled-perturbed density functional theory [J. Chem. Phys. 2013, 138, 174115] we calculate the magnetic exchange coupling parameters in a recently synthesized set of Fe7III disklike clusters [Inorg. Chem. 2011, 50, 3849–3851] to explain the unusually high ground-state spin found in the experiments. We show that the calculated exchange interactions for the new series of Fe7III disks present strikingly different trends compared to prior Fe7III disks. These differences are attributed to variations in the bridging ligands and the consequent structural changes in the complexes. The impact of these differences on the experimental ground-state spin of these complexes is rationalized using a simple classical spin model system and the calculated magnetic exchange couplings.

Performance Limitation of Microwave Assisted Magnetic Recording Combined With Exchange Coupled Composite Media Explored by Genetic Algorithm

A simple spin model combined with genetic algorithm showed the performance limitation of microwave assisted magnetic recording (MAMR) with multilayer media (MLM). Designs of MLM and MAMR were optimized so as to maximize the media thermal stability and the response of media magnetization to the external recording field. Tradeoff relationships between the two design objectives showed that higher AC-field is required for MLM than for the case in single-layer media. This is mainly because the condition for obtaining frequency matching between AC field and precession in each layer is difficult to achieve with the exchange coupling composite effect.

Fast passage dynamic nuclear polarization on rotating solids

Magic Angle Spinning (MAS) Dynamic Nuclear Polarization (DNP) has proven to be a very powerful way to improve the signal to noise ratio of NMR experiments on solids. The experiments have in general been interpreted considering the Solid-Effect (SE) and Cross-Effect (CE) DNP mechanisms while ignoring the influence of sample spinning. In this paper, we show experimental data of MAS-DNP enhancements of 1H and 13C in proline and SH3 protein in glass forming water/glycerol solvent containing TOTAPOL. We also introduce a theoretical model that aims at explaining how the nuclear polarization is built in MAS-DNP experiments. By using Liouville space based simulations to include relaxation on two simple spin models, {electron–nucleus} and {electron–electron–nucleus}, we explain how the basic MAS-SE-DNP and MAS-CE-DNP processes work. The importance of fast energy passages and short level anti-crossing is emphasized and the differences between static DNP and MAS-DNP is explained. During a single rotor cycle the enhancement in the {electron–electron–nucleus} system arises from MAS-CE-DNP involving at least three kinds of two-level fast passages: an electron–electron dipolar anti-crossing, a single quantum electron MW encounter and an anti-crossing at the CE condition inducing nuclear polarization in- or decrements. Numerical, powder-averaged, simulations were performed in order to check the influence of the experimental parameters on the enhancement efficiencies. In particular we show that the spinning frequency dependence of the theoretical MAS-CE-DNP enhancement compares favorably with the experimental 1H and 13C MAS-DNP enhancements of proline and SH3.

FORMATION OF MILLISECOND PULSARS FROM INTERMEDIATE- AND LOW-MASS X-RAY BINARIES

We present a systematic study of the evolution of intermediate- and low-mass X-ray binaries consisting of an accreting neutron star of mass $1.0-1.8 M_{\odot}$ and a donor star of mass $1.0-6.0 M_{\odot}$. In our calculations we take into account physical processes such as unstable disk accretion, radio ejection, bump-induced detachment, and outflow from the $L_{2}$ point. Comparing the calculated results with the observations of binary radio pulsars, we report the following results. (1) The allowed parameter space for forming binary pulsars in the initial orbital period - donor mass plane increases with increasing neutron star mass. This may help explain why some MSPs with orbital periods longer than $\sim 60$ days seem to have less massive white dwarfs than expected. Alternatively, some of these wide binary pulsars may be formed through mass transfer driven by planet/brown dwarf-involved common envelope evolution. (2) Some of the pulsars in compact binaries might have evolved from intermediate-mass X-ray binaries with anomalous magnetic braking. (3) The equilibrium spin periods of neutron stars in low-mass X-ray binaries are in general shorter than the observed spin periods of binary pulsars by more than one order of magnitude, suggesting that either the simple equilibrium spin model does not apply, or there are other mechanisms/processes spinning down the neutron stars.

Boiling Crisis as a Critical Phenomenon

We present the first experimental study of intermittency and avalanche distribution during a boiling crisis. To understand the emergence of power law statistics we propose a simple spin model capturing the measured critical exponent. The model suggests that behind the critical heat flux is a percolation phenomenon involving drying-rewetting competition close to the hot surface.

How anatomy shapes dynamics: a semi-analytical study of the brain at rest by a simple spin model

Resting state networks (RSNs) show a surprisingly coherent and robust spatiotemporal organization. Previous theoretical studies demonstrated that these patterns can be understood as emergent on the basis of the underlying neuroanatomical connectivity skeleton. Integrating the biologically realistic DTI/DSI-(Diffusion Tensor Imaging/Diffusion Spectrum Imaging)based neuroanatomical connectivity into a brain model of Ising spin dynamics, we found a system with multiple attractors, which can be studied analytically. The multistable attractor landscape thus defines a functionally meaningful dynamic repertoire of the brain network that is inherently present in the neuroanatomical connectivity. We demonstrate that the more entropy of attractors exists, the richer is the dynamical repertoire and consequently the brain network displays more capabilities of computation. We hypothesize therefore that human brain connectivity developed a scale free type of architecture in order to be able to store a large number of different and flexibly accessible brain functions.

Kaleidoscope of Exotic Quantum Phases in a FrustratedXYModel

The existence of quantum spin liquids was first conjectured by Pomeranchuk some 70 years ago, who argued that frustration in simple antiferromagnetic theories could result in a Fermi-liquid-like state for spinon excitations. Here we show that a simple quantum spin model on a honeycomb lattice hosts the long sought for Bose metal with a clearly identifiable Bose surface. The complete phase diagram of the model is determined via exact diagonalization and is shown to include four distinct phases separated by three quantum phase transitions.

Block Spin Ground State and Three-Dimensionality of(K,Tl)yFe1.6Se2

The magnetic properties and electronic structure of (K,Tl)y Fe1.6 Se2 is studied using first-principles calculations. The ground state is checkerboard antiferromagnetically coupled blocks of the minimal Fe4 squares, with a large block spin moment ~11.2{\mu}B . The magnetic interactions could be modelled with a simple spin model involving both the inter- and intra-block, as well as the n.n. and n.n.n. couplings. The calculations also suggest a metallic ground state except for y = 0.8 where a band gap ~400 - 550 meV opens, showing an antiferromagnetic insulator ground state for (K,Tl)0.8 Fe1.6 Se2 . The electronic structure of the metallic (K,Tl)y Fe1.6 Se2 is highly 3-dimensional with unique Fermi surface structure and topology. These features indicate that the Fe-vacancy ordering is crucial to the physical properties of (K,Tl)y Fe2-x Se2 .

Consistent model of magnetism in ferropnictides

The discovery of superconductivity in LaFeAsO introduced the ferropnictides as a major new class of superconducting compounds with critical temperatures second only to cuprates. The presence of magnetic iron makes ferropnictides radically different from cuprates. Antiferromagnetism of the parent compounds strongly suggests that superconductivity and magnetism are closely related. However, the character of magnetic interactions and spin fluctuations in ferropnictides, in spite of vigorous efforts, has until now resisted understanding within any conventional model of magnetism. Here we show that the most puzzling features can be naturally reconciled within a rather simple effective spin model with biquadratic interactions, which is consistent with electronic structure calculations. By going beyond the Heisenberg model, this description explains numerous experimentally observed properties, including the peculiarities of the spin wave spectrum, thin domain walls, crossover from first to second order phase transition under doping in some compounds, and offers new insight in the occurrence of the nematic phase above the antiferromagnetic phase transition.

Ground-State Properties of the Spin-1/2 Heisenberg-Ising Bond Alternating Chain with Dzyaloshinskii-Moriya Interaction

Quantum spin chains provide an excellent playground for theoretical studies of collective quantum phenomena as they may exhibit numerous exotic ground states and quantum critical points [1]. The spin-1/2 Heisenberg– Ising bond alternating chain, which has been originally invented by Lieb et al. [2] and recently re-examined by Yao et al. [3], represents a valuable example of rigorously solved quantum spin chain. The present work aims to provide a generalization of this simple but nontrivial quantum spin model by taking into account the antisymmetric Dzyaloshinskii–Moriya interaction.

Computer Simulations and Experimental Dynamical Characterization of a Composite Liquid Crystal-Polymer System

We present a Monte Carlo study of a liquid crystal-polymer interface, focusing on a single cell with boundary conditions tailored to mimic the main features of the system and we examine the effect of an external applied field. A simple lattice spin model, based on the Lebwohl-Lasher hamiltonian, has been employed to represent the nematic and the polymer molecules. The orientations of the spins representing the low molar mass nematic molecules are updated during the simulations while the polymer chain units are kept frozen. The model allows us to investigate the molecular organization and the ordering expected across the cell. Moreover the response to the change in external field intensity and duration pulse is also studied.

First principles theoretical study of complex magnetic order in transition‐metal nanowires

AbstractThe electronic and magnetic properties of one‐dimensional (1D) transition‐metal (TM) systems are investigated from a first principles theoretical perspective. The development of local magnetic moments and the stability of various collinear and non‐collinear spin arrangements are determined in the framework of a generalized gradient approximation to density‐functional theory (DFT). Two specific complementary problems are considered. The first one concerns the local moment formation in Cu wires doped with Co and Ni impurities. Recent results as a function of wire length, interatomic distances, impurity position within the wire, and total spin polarization $S_{z} $ are reviewed. It is shown that both Co and Ni impurities preserve their magnetic degree of freedom in monoatomic Cu wires by developing almost saturated local moments in all low‐lying total spin configurations ($S_{z} \leq 5/2$). The impurity moments are largely dominated by the d‐electron contributions. In the ground state they couple ferromagnetically with the moments induced at the Cu host atoms. The changes in the spin‐density distribution and in the local densities of electronic states are quantified as a function of the position of the impurity position within the wire. In addition, recent results on the ground‐state magnetic order in V nanowires are reviewed. The stability of ferromagnetic (FM), antiferromagnetic (AF), and spiral non‐collinear (NC) orders is analyzed in terms of the frozen‐magnon spectrum. A remarkable transition from FM to NC order is observed as a function of the nearest‐neighbor (NN) distance a. The dependence of the single‐particle electronic structure of the wire on the wave‐vector of the spin‐density wave (SDW) is demonstrated. Finally, the role of magnetic anisotropy on the stability of NC order is discussed in the framework of a simple classical spin model.

QCD-like theories at nonzero temperature and density

We investigate the properties of hot and/or dense matter in QCD-like theories with quarks in a (pseudo)real representation of the gauge group using the Nambu-Jona-Lasinio model. The gauge dynamics is modeled using a simple lattice spin model with nearest-neighbor interactions. We first keep our discussion as general as possible, and only later focus on theories with adjoint quarks of two or three colors. Calculating the phase diagram in the plane of temperature and quark chemical potential, it is qualitatively confirmed that the critical temperature of the chiral phase transition is much higher than the deconfinement transition temperature. At a chemical potential equal to half of the diquark mass in the vacuum, a diquark Bose-Einstein condensation (BEC) phase transition occurs. In the two-color case, a Ginzburg-Landau expansion is used to study the tetracritical behavior around the intersection point of the deconfinement and BEC transition lines, which are both of second order. We obtain a compact expression for the expectation value of the Polyakov loop in an arbitrary representation of the gauge group (for any number of colors), which allows us to study Casimir scaling at both nonzero temperature and chemical potential.

Tensor-entanglement renormalization group approach as a unified method for symmetry breaking and topological phase transitions

Traditional mean-field theory is a generic variational approach for analyzing symmetry breaking phases. However, this simple approach only applies to symmetry breaking states with short-range entanglement. In this paper, we describe a generic approach for studying two-dimensional (2D) quantum phases with long-range entanglement (such as topological phases). The method is based on (a) a general class of trial wave functions known as tensor-product states and (b) a 2D real-space renormalization group algorithm for efficiently calculating expectation values for these states. We demonstrate our method by studying several simple 2D quantum spin models exhibiting both symmetry breaking phase transitions and topological phase transitions. Our approach can be viewed as a unified mean-field theory for both symmetry breaking phases and topological phases.