Ising System Research Articles

Renormalization of quantum coherence and quantum phase transition in the Ising model

Quantifying quantum coherence of a given system not only plays an important role in quantum information science but also promotes our understanding of some basic problems, such as quantum phase transition. Conventional quantum coherence measures, such as l1-norm of coherence and relative entropy of coherence, are widely used to study quantum phase transition. Here we adopt a basis-independent coherence measure that is a quantum version of the Jensen–Shannon divergence to investigate the property of total quantum coherence, as well as its two contributions in quantum critical systems. Based on the quantum renormalization group method, we propose an analysis of the distribution of quantum coherence in the Ising system near the quantum critical point. We directly obtain the tradeoff relation, singular property, and scaling behavior in the Ising system. Furthermore, the monogamy relation is also studied in detail. These results further expand our understanding of quantum coherence as well as to enlarge the applications in using quantum coherence to reflect quantum critical phenomena.

Critical energy-density profile near walls

We examine critical adsorption for semi-infinite thermodynamic systems of the Ising universality class when they are in contact with a wall of the so-called normal surface universality class in spatial dimension d=3 and in the mean-field limit. We apply local-functional theory and Monte Carlo simulations in order to quantitatively determine the properties of the energy density as the primary scaling density characterizing the critical behaviors of Ising systems besides the order parameter. Our results apply to the critical isochore, near two-phase coexistence, and along the critical isotherm if the surface and the weak bulk magnetic fields are either collinear or anticollinear. In the latter case, we also consider the order parameter, which so far has yet to be examined along these lines. We find the interface between the surface and the bulk phases at macroscopic distances from the surface, i.e., the surface is "wet." It turns out that in this case the usual property of monotonicity of primary scaling densities with respect to the temperature or magnetic field scaling variable does not hold for the energy density due to the presence of this interface.

Out-of-time-ordered correlator in non-Hermitian quantum systems

We study the behavior of the out-of-time-ordered correlator (OTOC) in a non-Hermitian quantum Ising system. We show that the OTOC can diagnose not only the ground state exceptional point, which hosts the Yang-Lee edge singularity, but also the \textit{dynamical} exceptional point at the excited state. We find that the evolution of the OTOC in the parity-time symmetric phase can be divided into two stages: in the short-time stage, the OTOC oscillates periodically, and when the parameter is near the ground state exceptional point, this oscillation behavior can be described by both the scaling theory of the $(0+1)$D Yang-Lee edge singularity and the scaling theory of the $(1+1)$D quantum Ising model; while in the long-time stage the OTOC increases exponentially, controlled by the dynamical exceptional point. Possible experimental realizations are then discussed.

Kinetics of domain growth in Ising systems with bond disorder at regularly selected sites

We study the structure, phase behaviour and growth laws in Ising ferromagnets and binary mixtures with bond disorder introduced at regularly selected sites for a critical quench. The results presented here are from extensive Monte Carlo simulations on two-dimensional Ising systems. Domain growth in a ferromagnet is modelled by using nonconserved spin-flip (Glauber) kinetics, and phase separation in a binary (AB) mixture is modelled by conserved spin-exchange (Kawasaki) kinetics. In both cases, we observed that the domain growth law is consistent with the respective power-law growth with the variable growth exponent that depends on the number of disordered sites. The nonconserved Ising system follows dynamical scaling for all the number of disordered sites studied here; however, a small deviation is noticed for $$r\rightarrow 0$$ at a large number of disordered sites. Whereas, for the conserved case, dynamical scaling deviates from the master curve after a reasonable number of disordered lattice sites; we notice the formation of lamellar evolution morphology at a higher number of disordered sites at later times.

The accuracy of restricted Boltzmann machine models of Ising systems

Restricted Boltzmann machines (RBM) provide a general framework for modeling physical systems, but their behavior is dependent on hyperparameters such as the learning rate, the number of hidden nodes and the form of the threshold function. This article accordingly examines in detail the influence of these parameters on Ising spin system calculations. A tradeoff is identified between the accuracy of statistical quantities such as the specific heat and that of the joint distribution of energy and magnetization. The optimal structure of the RBM therefore depends intrinsically on the physical problem to which it is applied.

Dynamic magnetic properties of the mixed spin (1/2, 3/2) Ising system in the presence of magnetic field within the path probability method

The dynamic magnetic properties of the mixed spin (1/2, 3/2) Ising system with bilinear nearest-neighbor exchange interactions and a crystal-field term under the presence of the external longitudinal magnetic field (ELMF) are investigated by the path probability method. First we briefly examine the equilibrium magnetic properties of the system within the cluster variation method in order to clearly understand the dynamic behavior. In particular, we investigate thermal behavior of the magnetization in detail to search whether or not the metastable and unstable branches of magnetizations occur in the system. We find that the metastable and unstable branches of magnetization only exist if the system is in the presence of the ELMF. We also presented the metastable phase diagrams in the ELMF. Then, we apply the path probability method to the system and obtain the dynamic equations. Numerical solutions of these equations are given in the form of the flow diagrams (FDs). FDs explicitly illustrate the stable, metastable and unstable states as well as the role of the unstable states and initial conditions. FDs also display how one can obtain the metastable state more easily.

Protecting Spin Coherence in a Tunable Heisenberg Model.

Using an ensemble of atoms in an optical cavity, we engineer a family of nonlocal Heisenberg Hamiltonians with continuously tunable anisotropy of the spin-spin couplings. We thus gain access to a rich phase diagram, including a paramagnetic-to-ferromagnetic Ising phase transition that manifests as a diverging magnetic susceptibility at the critical point. The susceptibility displays a symmetry between Ising interactions and XY (spin-exchange) interactions of the opposite sign, which is indicative of the spatially extended atomic system behaving as a single collective spin. Images of the magnetization dynamics show that spin-exchange interactions protect the coherence of the collective spin, even against inhomogeneous fields that completely dephase the noninteracting and Ising systems. Our results underscore prospects for harnessing spin-exchange interactions to enhance the robustness of spin squeezing protocols.

Eigenvalues of Ising connection matrix with long-range interaction

We examine multidimensional Ising systems on hypercube lattices and calculate analytically the eigenvalues of their connection matrices. We express the eigenvalues in terms of spin–spin​ interaction constants and the eigenvalues of the one-dimensional Ising connection matrix (the latter are well known). To do this we present the eigenvectors as Kronecker products of the eigenvectors of the one-dimensional Ising connection matrix. For periodic boundary conditions, it is possible to obtain exact results for interactions with an arbitrary large number of neighboring spins. We present exact expressions for the eigenvalues for two- and three-dimensional Ising connection matrices accounting for the first five coordination spheres (that is interactions up to next-next-next-next nearest neighbors). In the case of free-boundary systems, we show that in the two and three dimensions the exact expressions could be obtained only if we account for interactions with spins of not more than first three coordination spheres.

Configurational mean-field reduced transfer matrix method for Ising systems

A mean-field method for the hypercubic nearest-neighbor Ising system is introduced and applications to the method are demonstrated. The main idea of this work is to combine the Kadanoff’s mean-field approach with the model presented by one of us previously. The mean-field approximation is introduced with the replacement of the central spin in Ising Hamiltonian with an average value of particular spin configuration, i.e, the approximation is taken into account within each configuration. This approximation is used in two different mean-field-type approaches. The first consideration is a pure-mean-field-type treatment in which all the neighboring spins are replaced with the assumed configurational average. The second consideration is introduced by the reduced transfer matrix method. The estimations of critical coupling values of the systems are evaluated both numerically and also analytically by the using of saddle point approximation. The analytic estimation of critical values in the first and second considerations are [Formula: see text] and [Formula: see text] respectively. Obviously, both of the considerations have some significant deviation from the exact treatment. In this work, we conclude that the method introduced here is more appropriate physical picture than self-consistent mean-field-type models, because the method introduced here does not presume the presence of the phase transition from the outset. Consequently, the introduced approach potentially makes our research very valuable mean-field-type picture for phase transition treatment.

Ground states, residual entropies, and specific heat capacity properties of frustrated Ising system on pyrochlore lattice in effective field theory cluster approximations

The thermodynamics of the antiferromagnetic spin-1∕2 Ising model in the presence of the external magnetic field on the geometrically frustrated pyrochlore lattice is investigated using various effective field theory cluster approximations up to the cluster size consisting of 7 sites in the form of two site-connected elementary tetrahedrons. The system of all ground states of the model is determined and the dependence of the magnetization, of the specific heat capacity, as well as of the entropy of the model on the used cluster approximation is investigated. It is shown that the thermodynamic properties of the ground states depend on the used cluster approximation and tend to those obtained in the framework of other theoretical approaches with the increasing of the cluster size. The analysis shows that, although it seems that the EFT cluster approximation represents quite effective approach for the investigation of properties of the model for some specific intervals and discrete values of the external magnetic field, in general, one must be very careful when interpreting obtained results. The dependence of the critical temperature, of the spontaneous magnetization, as well as of the specific heat capacity of the ferromagnetic model on the used cluster approximation is also discussed.

Dynamic critical phenomena in a multilayer Ising system

Using the mixed-spin system, we precisely calculate the dynamic critical phenomena, namely dynamic compensation behaviors, dynamic phase diagrams and dynamic hysteresis loops in a multilayer Ising system that composes of four monoatomic layers. As the method, we use the mean-field theory based on Glauber-type stochastic dynamics. It is found that the Hamiltonian parameters have a strong effect on the dynamic critical phenomena. The system displays the P-, Q-, R-, and S-type compensations and multiple hysteresis loop behaviors. The results are qualitatively consistent with those of some theoretical and experimental studies.

Distinguishing the Intrinsic Antiferromagnetism in Polycrystalline LiCoPO4 and LiMnPO4 Olivines.

We report a detailed investigation of the long-range magnetic ordering in polycrystalline samples of LiCoPO4 and LiMnPO4, which belong to a series of well-known olivine cathode materials LiMPO4 (M = Mn, Fe, Co, Ni). Samples were prepared by hydrothermal and solid state methods. The magnetic susceptibility is found to be strongly field-dependent, impacting the antiferromagnetic transition temperature and the bifurcation of the FC and ZFC curves. We discuss the role synthesis conditions have on impurity formation and particle size. We report neutron powder diffraction data for the samples prepared by solid state methods. Based upon representational analysis of the observed reflections, we affirm the magnetic structure Pnma' for LiCoPO4 and Pn'm'a' for LiMnPO4. The refined magnetic moments from these models are 3.28(4) μB for LiCoPO4 and 4.28(3) μB for LiMnPO4. We also study the onset of magnetic ordering in each sample and affirm that the ordering temperature is 22 K for LiCoPO4 and 34 K for LiMnPO4. The critical parameters describing those transitions are βc = 0.21(4) (LiCoPO4) and βc = 0.31(3) (LiMnPO4). These values are characteristic of a 3D Ising system for LiMnPO4 and intermediate behavior between a 2D and 3D Ising system for LiCoPO4. We compare these observations with other reports proposing lower magnetic symmetry.

Investigations on the magnetic properties of the Fe5-xCoxSiB2 alloys by experimental and band structure calculation methods

We present theoretical and experimental investigations on the electronic and magnetic properties of the Fe5-xCoxSiB2 alloys (x = 0, 0.5, 1.0, 1.5, 2.5 and 5). Theoretical calculations show the dependence of the magnetic properties (magnetic moments, magneto-crystalline anisotropy, exchange-coupling parameters, Curie temperature) on the Fe/Co ratio and preferential occupation of Co atoms for 16l crystallographic site. The spontaneous magnetization as a function of temperature was measured and fitted using the Kuz'min function and modified Arrott-Belov plots. The first procedure shows the decrease of the spontaneous magnetization at 0 K with Co content, with obtained values between 8.79 µB/f.u. (x = 0) and 5.97 µB/f.u. (x = 1.5), in agreement with the theoretical calculations. Also, by thermo-magnetic measurements fitted using Kuz’min function Curie temperatures (Tc) have been obtained, which decrease with the Co content, from 845 K (x = 0) to 667 K (x = 1.5). According to the theoretical exchange-coupling parameters calculated for both Fe spins, the decrease of the Tc is mainly related to the decrease of the Fe 16l–Fe 16l exchange interaction. Moreover, the evolution of the magneto-crystalline anisotropy energy (MAE) with Co content shows good agreement between theoretical and experimental investigations. The 3d magnetism character is found to evolve from well localized behavior in the Fe5SiB2 compound, featured by critical exponents typical of Ising systems, to more delocalized upon Co for Fe substitution with larger range interactions and modified critical exponents.This study provides an insight regarding the influence of the Co doping on the stoichiometry and on the magnetic properties of the Fe5-xCoxSiB2 alloys, which have been previously suggested as good candidates for obtaining rare-earth free permanent magnets with enhanced MAE and higher coercivity.

Dynamic magnetic hysteresis loop behaviors of a mixed spin (2, 5/2) Ising model on two interpenetrating square lattices

We investigate dynamic magnetic hysteresis loop (DMHL) behaviors of a mixed spin (2, 5/2) Ising model on two interpenetrating square lattices under an oscillating magnetic field within the effective-field theory based on Glauber–type stochastic dynamics. We study the DMHL properties for various values of reduced temperatures (T/zJ), crystal-field interaction (D/zJ) and frequency () of the magnetic field. We also examine T/zJ, D/zJ and dependences of the coercive fields (CFs) and remanent magnetizations (RMs). We found that for very low and high values of T/zJ and D/zJ, the hysteresis loop area is narrower and thinner that correspond soft magnets that desirable for transformers and motor cores and AC applications. We observed that for high values of the hysteresis loop areas are wide and big that corresponds hard magnets which can be useful for permanent magnets, magnetic recording, small motors and magnetic locks. We also found that the DMHLs, CFs and RMs behaviors are in quantitatively good agreement with some theoretical for Ising systems and experimental works for magnetic materials, such as cobalt films, Fe films and some magnetic nanomaterials.

Cluster size effects in the magnetic properties of [formula omitted]-[formula omitted] alloys

A spin-1/2 Ising model, defined in the body centered cubic lattice, is used to describe some of the thermodynamic properties of Fep-Alq alloys, with p+q=1. The model assumes, besides the nearest-neighbor exchange coupling, the existence of further next-nearest-neighbor superexchange interactions, where the latter ones depend on the aluminum atoms cluster size. The Ising system so considered is studied by employing Monte Carlo simulations, using a hybrid algorithm consisting of one single-spin Metropolis move together with one single-cluster Wolff algorithm allied, in addition, with single histograms procedures and finite-size scaling techniques. Quite good fits to the experimental results of the ordering critical temperature, as a function of Al concentration in the range 0⩽q<0.7, are obtained and compared to more recent theoretical approaches done on the same alloys.

Magnetization plateaus in a frustrated spin ½ four-leg nanotube

The magnetic behavior of the spin - ½ Ising system, consisting of a squared four-legs Nanotube connected to each other by different exchange couplings, have been studied by mean of the effective field theory (EFT). The Nano-system can be immersed in an applied homogenous magnetic field. In addition to the transversal J⊥ and longitudinal J//interactions, we attentively examine the influence of the diagonal exchange interaction Jd on the main thermodynamic variables such as internal energy, spontaneous magnetization, isothermal magnetization, and initial susceptibility.The results show that critical temperature is enhanced with increasing the diagonal exchange coupling strength, while the isothermal magnetization curves can display jumps and plateaus at special values of the applied field, especially at lower temperatures. Our study proves also that the sign and the strength of each exchange coupling constant play a key role in the global magnetic behavior of this single-wall squared Nanotube spin. In particular, antiferromagnetic diagonal exchange interaction can lead to strong frustration.

Cell death and survival due to cytotoxic exposure modelled as a two-state Ising system.

Cancer chemotherapy agents are assessed for their therapeutic utility primarily by their ability to cause apoptosis of cancer cells and their potency is given by an IC50 value. Chemotherapy uses both target-specific and systemic-action drugs and drug combinations to treat cancer. It is important to judiciously choose a drug type, its dosage and schedule for optimized drug selection and administration. Consequently, the precise mathematical formulation of cancer cells' response to chemotherapy may assist in the selection process. In this paper, we propose a mathematical description of the cancer cell response to chemotherapeutic agent exposure based on a time-tested physical model of two-state multiple-component systems near criticality. We describe the Ising model methodology and apply it to a diverse panel of cytotoxic drugs administered against numerous cancer cell lines in a dose–response manner. The analysed dataset was generated by the Netherlands Translational Research Center B.V. (Oncolines). This approach allows for an accurate and consistent analysis of cytotoxic agents' effects on cancer cell lines and reveals the presence or absence of the bystander effect through the interaction constant. By calculating the susceptibility function, we see the value of IC50 coinciding with the peak of this measure of the system's sensitivity to external perturbations.

Phase Transitions in the Two-Dimensional Ising Model from the Microcanonical Perspective

The continuous ferromagnetic-paramagnetic phase transition in the two-dimensional Ising model has already been excessively studied by conventional canonical statistical analysis in the past. We use the recently developed generalized microcanonical inflection-point analysis method to investigate the least-sensitive inflection points of the microcanonical entropy and its derivatives to identify transition signals. Surprisingly, this method reveals that there are potentially two additional transitions for the Ising system besides the critical transition.

Phase space classification of an Ising cellular automaton: The Q2R model

An exact classification of the different dynamical behaviors that exhibits the phase space of a reversible and conservative cellular automaton, the so-called Q2R model, is shown in this paper. Q2R is a cellular automaton which is a dynamical variation of the Ising model in statistical physics and whose space of configurations grows exponentially with the system size. As a consequence of the intrinsic reversibility of the model, the phase space is composed only by configurations that belong to a fixed point or a cycle. In this work, we classify them in four types accordingly to well differentiated topological characteristics. Three of them –which we call of type S-I, S-II, and S-III– share a symmetry property, while the fourth, which we call of type AS does not. Specifically, we prove that any configuration of Q2R belongs to one of the four previous types of cycles. Moreover, at a combinatorial level, we can determine the number of cycles for some small periods which are almost always present in the Q2R. Finally, we provide a general overview of the resulting decomposition of the arbitrary size Q2R phase space and, in addition, we realize an exhaustive study of a small Ising system (4 × 4) which is thoroughly analyzed under this new framework, and where simple mathematical tools are introduced in order to have a more direct understanding of the Q2R dynamics and to rediscover known properties like the energy conservation.

Simulation of an extended 3D mixed Ising model by Monte Carlo method

Owing to their useful properties, the ferromagnetic mixed spins Ising have been extensively investigated. In this context, the paper aims to study the phase diagram of 3d mixed spin-1 and spin-3/2 Ising system and its critical properties. The adapted Hamiltonian of the considered mixed spin-(1, 3/2) Ising model is parameterized by three exchange interaction between first nearest neighbors spins Ji (with i = 1, 2 and 3), two crystal field interactions and the external magnetic field. The competition between these parameters can generate rich critical behavior with the coexistence of several phases in the ground state phase diagram.In this work, Monte Carlo simulation based on Metropolis algorithm, was used to study the critical properties in different phases of ground state. The analysis of the behavior of total magnetization and susceptibility as a function of temperature allowed us to study the behavior of the critical temperature of the ferromagnetic – paramagnetic transition TC as a function of different parameters. The obtained results shows that the critical temperature TC has linear Ji dependency in strong spin–spin interaction regime.