Inference of Kinetic Ising Model on Sparse Graphs

Based on dynamical cavity method, we propose an approach to the inference of kinetic Ising model, which asks to reconstruct couplings and external fields from given time-dependent output of original system. Our approach gives an exact result on tree graphs and a good approximation on sparse graphs, it can be seen as an extension of Belief Propagation inference of static Ising model to kinetic Ising model. While existing mean field methods to the kinetic Ising inference e.g., naïve mean-field, TAP equation and simply mean-field, use approximations which calculate magnetizations and correlations at time t from statistics of data at time t?1, dynamical cavity method can use statistics of data at times earlier than t?1 to capture more correlations at different time steps. Extensive numerical experiments show that our inference method is superior to existing mean-field approaches on diluted networks.     

Effects of the randomly distributed magnetic field on the phase diagrams of the Ising Nanowire II: Continuous distributions

The effect of the random magnetic field distribution on the phase diagrams and ground state magnetizations of the Ising nanowire has been investigated with effective field theory with correlations. Gaussian distribution has been chosen as a random magnetic field distribution. The variation of the phase diagrams with that distribution parameters has been obtained and some interesting results have been found such as disappearance of the reentrant behavior and first order transitions which appear in the case of discrete distributions. Also for single and double Gaussian distributions, ground state magnetizations for different distribution parameters have been determined which can be regarded as separate partially ordered phases of the system.     

Properties of the ground state in a spin-2 transverse Ising model with the presence of a crystal field

The properties of the ground state in the spin-2 transverse Ising model with the presence of a crystal field are studied by using the effective-field theory with correlations. The longitudinal and transverse magnetizations, the phase diagram and the internal energy in the ground state are given numerically for a honeycomb lattice (z=3).     

Inverse statistical problems: from the inverse Ising problem to data science

Inverse problems in statistical physics are motivated by the challenges of ‘big data’ in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.     

The study of magnetization of the spin system in the ground state

Within the framework of the effective-field theory with self-spin correlations and the differential operator technique, the ground state magnetizations of the biaxial crystal field spin system on the honeycomb lattices have been studied. The influences of the biaxial crystal field on the magnetization in the ground state have been investigated in detail.     

Odd triplet pairing in clean superconductor/ferromagnet heterostructures

We study triplet pairing correlations in clean ferromagnet (F)/superconductor (S) nanojunctions, via fully self-consistent solution of the Bogoliubov-de Gennes equations. We consider FSF trilayers, with S being an s-wave superconductor, and an arbitrary angle alpha between the magnetizations of the two F layers. We find that contrary to some previous expectations, triplet correlations, odd in time, are induced in both the S and F layers in the clean limit. We investigate their behavior as a function of time, position, and alpha. The triplet amplitudes are largest at times on the order of the inverse Debye frequency, and at that time scale they are long-ranged in both S and F. The zero temperature condensation energy is found to be lowest when the magnetizations are antiparallel.     

Effects of the randomly distributed magnetic field on the phase diagrams of Ising nanowire I: Discrete distributions

The effect of the random magnetic field distribution on the phase diagrams and ground state magnetizations of Ising nanowire is investigated using effective field theory with correlations. Trimodal distribution has been chosen as a random magnetic field distribution. The variation of the phase diagrams with that distribution parameters has been obtained and some interesting results have been found such as reentrant behavior and first order transitions. Also for the trimodal distribution, ground state magnetizations for different distribution parameters have been determined which can be regarded as separate partially ordered phases of the system.     

Frustration signatures in the anisotropic model of a nine-spin <Emphasis Type="Italic">s</Emphasis> = 3/2 ring with bond defect

Effects of magnetic frustration in the model of nine-membered antiferromagnetic s = 3/2 molecular spin ring are investigated. We use a Heisenberg spin model with nearest-neighbor interactions, single-ion anisotropy and with tunable bond defect leading to continuously varying topology: from closed to open ring. In order to identify a frustrated phase we calculate the full energy spectrum of the model and a number of thermodynamic quantities at low temperature. The calculations are performed by means of numerically exact methods: quantum transfer matrix and exact diagonalization. It is shown that total and local magnetizations, nearest-neighbor spin correlations and spin fluctuations can serve as consistent frustration signatures. Magnetizations and spin-spin correlations are reduced in the frustrated phase whereas fluctuations and correlations of fluctuations increase. The ground state in a frustrated phase is a m = 1/2 doublet and in the non-frustrated phase a m = 3/2 doublet. In the system studied bipartiteness is not opposite to frustration as there are regions in the parameter space for which the system is neither bipartite nor frustrated.     

Dynamic magnetic properties of the kinetic cylindrical Ising nanotube

The nature (time variation) of response magnetizations m(wt) of the kinetic cylindrical Ising nanotube in the presence of a periodically varying external magnetic field h(wt) is studied by employing the effective-field theory (EFT) with correlations as well as the Glauber-type stochastic dynamics. We have determined the time variations of m(wt) and h(wt) for various temperatures, and investigated the dynamic magnetic hysteresis behavior. Temperature dependence of the dynamic magnetizations, hysteresis loop areas and correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic transitions as well as to obtain the dynamic phase transition temperatures. We also present the dynamic phase diagrams in the three different planes and compare the results of the equilibrium and nonequilibrium states. The phase diagrams exhibit dynamic tricritical, isolated critical, multicritical and triple points. The results are in good agreement with some experimental and theoretical results.     

Error Estimation in the Histogram Monte Carlo Method

We examine the sources of error in the histogram reweighting method for Monte Carlo data analysis. We demonstrate that, in addition to the standard statistical error which has been studied elsewhere, there are two other sources of error, one arising through correlations in the reweighted samples, and one arising from the finite range of energies sampled by a simulation of finite length. We demonstrate that while the former correction is usually negligible by comparison with statistical fluctuations, the latter may not be, and give criteria for judging the range of validity of histogram extrapolations based on the size of this latter correction.     

Effects of selective dilution on phase diagram and ground-state magnetizations of an Ising antiferromagnet on triangular and honeycomb lattices

We employ an effective-field theory with correlations in order to study the phase diagram and ground-state magnetizations of a selectively diluted Ising antiferromagnet on triangular and honeycomb lattices. Dilution of different sublattices with generally unequal probabilities results in a rather intricate phase diagram in the sublattice dilution parameters space. In the case of the frustrated triangular lattice antiferromagnet the selective dilution affects the degree of frustration which can lead to some peculiar phenomena, such as reentrant behavior of long-range order or unsaturated sublattice magnetizations at zero temperature. The selectively diluted Ising antiferromagnet on the honeycomb lattice is obtained as a special case when one sublattice of the triangular lattice is completely removed by dilution.     

Frustration in a transverse Ising nanoisland: effects of interlayer coupling

The phase diagram and magnetizations in a transverse Ising nanoisland are examined by using the effective field theory with correlations. The nanoisland is constructed from two layers with nine atoms in each which are coupled by the interlayer coupling. We present some characteristic phenomena in them which come from the frustration induced by an interlayer coupling and two transverse fields.     

Optimization of spin-triplet supercurrent in ferromagnetic Josephson junctions

We have observed long-range spin-triplet supercurrents in Josephson junctions containing ferromagnetic (F) materials, which are generated by noncollinear magnetizations between a central Co/Ru/Co synthetic antiferromagnet and two outer thin F layers. Here we show that the spin-triplet supercurrent is enhanced up to 20 times after our samples are subject to a large in-plane field. This occurs because the synthetic antiferromagnet undergoes a "spin-flop" transition, whereby the two Co layer magnetizations end up nearly perpendicular to the magnetizations of the two thin F layers. We report direct experimental evidence for the spin-flop transition from scanning electron microscopy with polarization analysis and from spin-polarized neutron reflectometry. These results represent a first step toward experimental control of spin-triplet supercurrents.     

Edge magnetization in Bernal-stacked trilayer zigzag graphene nanoribbons

We have used a tight-binding Hamiltonian of an ABA-stacked trilayer zigzag graphene nanoribbon with β-alignment edges to study the edge magnetizations. Our model includes the effect of the intralayer next-nearest-neighbor hopping, the interlayer hopping responsible for the trigonal warping and the interaction between electrons, which is considered by a single band Hubbard model in the mean field approximation. Firstly, in the neutral system we analyzed the two magnetic states in which both edge magnetizations reach their maximum value; the first one is characterized by an intralayer ferromagnetic coupling between the magnetizations at opposite edges, whereas in the second state that coupling is antiferromagnetic. The band structure, the location of the edge-state bands and the local density of states resolved in spin are calculated in order to understand the origins of the edge magnetizations. We have also introduced an electron doping so that the number of electrons in the ribbon unit cell is higher than in neutral case. As a consequence, we have obtained magnetization steps and charge accumulation at the edges of the sample, which are caused by the edge-state flat bands.     

Magnetic properties of bilayer nano-stanene-like structure with Ruderman–Kittel–Kasuya–Yoshida coupling

A bilayer nano-stanene-like structure with Ruderman–Kittel–Kasuya–Yoshida (RKKY) coupling described by the Ising model is proposed. The magnetic and thermodynamic properties are studied using the effective-field theory with correlations. The exchange coupling, longitudinal magnetic field, number of non-magnetic layers, and anisotropies had major influences on the magnetization, specific heat, and internal energy. Different saturation magnetizations are observed on the magnetization curve. The variation in the system blocking temperature is studied. The results provide theoretical guidance for the magnetic investigation of nanomaterials with RKKY coupling.     

Hysteresis behaviors in a cylindrical Ising nanowire

The hysteresis behaviors of the cylindrical Ising nanowire are investigated within the effective-field theory with correlations at temperatures below, around and above the critical temperature. The hysteresis curves are obtained for different reduced temperatures both ferromagnetic and antiferromagnetic interactions between the shell and the core. We find that the hysteresis loop areas decrease when the reduced temperatures increase, and the hysteresis loops disappear at certain reduced temperatures. Moreover, for the antiferromagnetic nanowire the hysteresis loop areas disappear earlier than the ferromagnetic case as the reduced temperature increases. An unusual form of triple hysteresis behaviors is observed for the antiferromagnetic nanowire system. The thermal behaviors of the coercivities and remanent magnetizations are also investigated. The results are in good agreement with some experimental and theoretical results.     

Ising nanowires with simple core–shell structure; Their characteristic phenomena

The phase diagrams and magnetizations of Ising nanowires with simple core–shell structure are investigated by the use of the effective field theory with correlations. A lot of characteristic behaviors observed in ferromagnetic and ferrimagnetic materials as well as novel phenomena have been obtained, although one section of the system is consisted of one spin-1/2 surface shell atom and one spin-1/2 core atom and they are coupled with a positive or a negative shell–core exchange interaction.     

Phase diagrams in an Ising nanotube (or nanowire) with a diluted surface; Effects of interlayer coupling at the surface

The phase diagrams and magnetizations of two nanosystems (nanotube and nanowire) with a dilution at the surface are investigated by the use of the effective field theory with correlations. In particular, the effects of interlayer coupling between the surface and the core on them are discussed for the two systems. Some interesting phenomena have been found in the phase diagrams and the thermal variations of magnetizations, especially for the nanotube with a very high dilution and the possibility of two compensation points in the nanowire with a small interlayer coupling.     

Effective-field theory of the Ising model with three alternative layers on the honeycomb and square lattices

The Ising model with three alternative layers on the honeycomb and square lattices is studied by using the effective-field theory with correlations. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the adjacent spins of the nearest-neighbor layers are coupled either ferromagnetically or anti-ferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the thermal variations of the magnetizations and present the phase diagrams. The phase diagrams contain the paramagnetic, ferromagnetic and anti-ferromagnetic phases, and the system also exhibits a tricritical behavior.     

Magnetic Properties of Ferromagnetic Double Layers with Ferrimagnetic Interlayer Coupling at Zero Temperature

Spin-wave theory is used to study magnetic properties of ferromagnetic double layers with a ferrimagnetic interlayer coupling at zero temperature. The spin-wave spectra and four sublattices magnetizations and internal energy are calculated by employing retarded Green function technique. The sublattice magnetizations at ground state are smaller than their classical values, owing to the zero-point quantum fluctuations of the spins.