Extended Ising Model Research Articles

Magnetization processes and magnetocaloric effect of the Ising model on the octahedral lattice

The magnetocaloric effect and magnetization processes of the extended Ising model on the 3-dimensional octahedral lattice are studied by the classical Monte Carlo method with Metropolis algorithm. It is shown that different combinations of antiferromagnetic and ferromagnetic nearest-neighbor interactions J1 and J2 (in particular J1=−1, J2=1 and J1=−1, J2=−1) lead to the fundamentally different magnetic behaviors at nonzero temperatures, despite the fact that zero-temperature magnetization curves have exactly the same form. The reason is that the spin configurations forming zero-temperature magnetization plateaus for both J2=−1 and J2=1 are different, and different are also their temperature evolutions (controlled by calculations of in-plane and inter-plane sublattice magnetizations), which lead to different results for the magnetic entropy change (the magnetocaloric effect). Due to this fact a much higher positive entropy change is observed for the ferro-antiferromagnetic system compared to the pure antiferromagnetic system.

Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions

The quantum long-range extended Ising model possesses several striking features which cannot be observed in the corresponding short-range model. We report that the pattern obtained from the entanglement between any two arbitrary sites of the long-range model can be mimicked by the model having a finite range of interactions provided the interaction strength is moderate. On the other hand, we illustrate that when the interactions are strong, the entanglement distribution in the long-range model does not match the class of a model with a few interactions. We also show that the monogamy score of entanglement is in good agreement with the behavior of pairwise entanglement. Specifically, it saturates when the entanglement in the finite-range Hamiltonian behaves similarly to the long-range model, while it decays algebraically otherwise.

Quantum nonlocality and topological quantum phase transitions in the extended Ising chain

We use two-site quantum nonlocality to identify the topological quantum phase transitions (TQPTs) of the extended Ising model driven by varying system parameters. We investigate how the system parameters, including the anisotropies of the nearest-neighbor and the next-nearest-neighbor spin pairs, the transverse magnetic field, and the three-spin interaction, affect the quantum nonlocality. We show that the nonlocality cannot mark any TQPTs while its first derivative can perfectly characterize the TQPTs. By making the influences of the thermal fluctuations and the site distance of spin pairs on the critical behavior of the TQPTs analysis, we show that the sufficiently low temperature has a slight impact on the features of nonlocality and its first derivative while the site distance of spin pairs can significantly alter the properties of nonlocality and its first derivative. We further present the energy spectra and the trajectories of the winding vectors of the model to demonstrate that the quantum nonlocality can be employed to successfully signalize the TQPTs.

The extended Ising model Hamiltonian for order-disorder phase transition on the clean Si (001) surface

We investigated the order-disorder phase transitions with the four spin interacting Ising model Hamiltonian, which was obtained using first principle calculation results for the Si(100) surface. This is the first proposed effective spin Hamiltonian for dimer configurations. However, the four spin interacting Hamiltonian has not been established to date. All simulations were performed using the cellular automaton algorithm adapted for this Hamiltonian. As a result of the simulations made for three different parameter sets, the order-disorder phase transition temperature on the clean Si(001) surface was obtained on average at 203±4 K, which is consistent with the experimental results.

Quantum speed limit and topological quantum phase transition in an extended [formula omitted] model

We explore quantum speed limit time τQSL of a qubit system coupling to a spin chain environment which is described by an extended Ising model associated with non-trivial topological characterization. For an initial pure state, we find that τQSL exhibits a behavior of local maximum around all critical points when the environment spin chain undergoes a topological quantum phase transition driven by external magnetic field λ or the anisotropy γ of nearest-neighbor interaction. And the value of local maximum would increase by strengthening the coupling between the system and environment around the critical points. However, the behavior of τQSL are both driving parameters and critical points dependent when the topological quantum phase transition is driven by the three-site interaction α or its anisotropy δ. Additionally, we also investigate τQSL for arbitrary time-evolution state in the whole dynamics process and find that τQSL exhibits a behavior of oscillation at non-critical points. However, τQSL will decay rapidly to zero around all critical points, and such trend accompany with oscillation behavior at some critical points.

Anisotropic Effect on Local Magnetic Properties of 3D Extended Ising Model

The magnetic properties of anisotropic 3D Ising model on a cubic lattice are studied by Monte Carlo simulation. In particular, we have considered an extended 3D Ising model with spatially uniaxial anisotropic bond randomness on the simple cubic lattice parameterized by exchange interaction parameter [Formula: see text], anisotropy parameter [Formula: see text] and external longitudinal magnetic field [Formula: see text]. The obtained numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model at critical temperature [Formula: see text] that is strongly correlated to [Formula: see text] and [Formula: see text]. Especially, in the limit, [Formula: see text], the spin ½ cubic lattice becomes a collection of noncorrelated Ising chains, whereas in the other limit, [Formula: see text], the system becomes a stack of noncorrelated Ising square lattice.

Modeling of magnetic Barkhausen noise for layered ferromagnetic materials based on extended Ising model with double Boltzmann function

Modeling of magnetic Barkhausen noise for layered ferromagnetic materials based on extended Ising model with double Boltzmann function

Magnetization plateaus and phase diagrams of the extended Ising model on the Shastry-Sutherland lattice: effects of long-range interactions

Magnetization plateaus and phase diagrams of the extended Ising model on the Shastry-Sutherland lattice with the first $(J_1)$, second $(J_2)$, third $(J_3)$ fourth $(J_4)$ and fifth $(J_5)$ nearest-neighbour spin couplings are studied by the classical Monte Carlo method. It is shown that switching on $J_4$ and $J_5$ interactions (in addition to usually considered $J_1, J_2$ and $J_3$ interactions) changes significantly the picture of magnetization processes found for $J_4=J_5=0$ and leads to stabilization of new macroscopic magnetic phases (plateaus) with fractional magnetization. In particular, it is found that combined effects of $J_4$ and $J_5$ interactions generate the following sequence of plateaus with the fractional magnetization: $m/m_s$=1/9, 1/6, 2/9, 1/3, 4/9, 1/2, 5/9 and 2/3. The results obtained are consistent with experimental measurements of magnetization curves in selected rare-earth tetraborides.

One-way deficit and quantum phase transitions in XY model and extended Ising model

Originating in questions regarding work extraction from quantum systems coupled to a heat bath, quantum deficit, a kind of quantum correlations besides entanglement and quantum discord, links quantum thermodynamics with quantum correlations. In this paper, we evaluate the one-way deficit of two adjacent spins in the bulk for the $XY$ model and its extend model: the extended Ising model. We find that the one-way deficit susceptibility is able to characterize the quantum phase transitions in the $XY$ model and even the topological phase transitions in the extend Ising model. This study may enlighten extensive studies of quantum phase transitions from the perspective of quantum information processing and quantum computation, including finite-temperature phase transitions, topological phase transitions and dynamical phase transitions of a variety of quantum many-body systems.

Dynamical quantum phase transitions in extended transverse Ising models

We study the dynamical quantum phase transitions (DQPTs) manifested in the subsequent unitary dynamics of an extended Ising model with additional three spin interactions following a sudden quench. Revisiting the equilibrium phase diagram of the model where different quantum phases are characterised by different winding numbers, we show that in some situations the winding number may not change across a gap closing point in the energy spectrum. Although, usually there exists a one-to-one correspondence between the change in winding number and the number of critical time scales associated with DQPTs, we show that the extended nature of interactions may lead to unusual situations. Importantly, we show that in the limit of the cluster Ising model, three critical modes associated with DQPTs become degenerate and thereby leading to a single critical time scale for a given sector of Fisher zeros.

Quantum correlation and quantum phase transition in the one-dimensional extended Ising model

Quantum phase transitions can be understood in terms of Landau’s symmetry-breaking theory. Following the discovery of the quantum Hall effect, a new kind of quantum phase can be classified according to topological rather than local order parameters. Both phases coexist for a class of exactly solvable quantum Ising models, for which the ground state energy density corresponds to a loop in a two-dimensional auxiliary space. Motivated by this we study quantum correlations, measured by entanglement and quantum discord, and critical behavior seen in the one-dimensional extended Ising model with short-range interaction. We show that the quantum discord exhibits distinctive behaviors when the system experiences different topological quantum phases denoted by different topological numbers. Quantum discords capability to detect a topological quantum phase transition is more reliable than that of entanglement at both zero and finite temperatures. In addition, by analyzing the divergent behaviors of quantum discord at the critical points, we find that the quantum phase transitions driven by different parameters of the model can also display distinctive critical behaviors, which provides a scheme to detect the topological quantum phase transition in practice.

Fractional magnetization plateaus in the extended Ising model on the Shastry-Sutherland lattice: Application to rare-earth metal tetraborides

The classical Monte Carlo method is used to examine possibilities of formation of magnetization plateaus in the extended Ising model with the first , second , third , and fourth nearest-neighbour spin couplings on the Shastry–Sutherland lattice. It is shown that in the limit of ferromagnetic interaction the combined effects of and lead to the stabilization of the magnetization plateau against the standard Ising plateau (where is the saturation magnetization). At some critical values of and interactions the plateau phase is fully removed from the ground-state phase diagram providing a possible explanation of the fact that in some rare-earth tetraborides this phase is present and in some completely absent. In the opposite limit of antiferromagnetic interaction the model provides a reach spectrum of magnetic solutions, where in addition to the standard magnetization plateau one can find the following sequence of plateaus with the fractional magnetization: =1/10, 1/9, 1/6, 1/5, 2/5, 4/9, 7/15, and 5/9. The results obtained are consistent with experimental measurements of magnetization curves in selected rare-earth tetraborides.

Ground-State Phase Diagram of the Extended Ising Model on the Shastry-Sutherland Lattice

on the Shastry-Sutherland Lattice H. ƒen£arikovaa,∗, P. Farka2ovský and P. Puchala Institute of Experimental Physics SAS, Watsonova 47, 040 01 Ko2ice, Slovakia Institute of Physics, Faculty of Sciences, P. J. ’afarik University, Park Angelinum 9, 041 54 Ko2ice, Slovakia The ground-state phase diagram of the Ising model on the Shastry-Sutherland lattice with the rst (J1), second (J2), third (J3) and fourth (J4) nearest neighbour spin couplings is studied using the exact and well controlled numerical method. It is shown that switching on of the J3 and J4 interactions (in addition to usually considered J1 and J2 interactions) leads to stabilization of the following dominant magnetic phases with m/ms = 1/9, 1/6, 4/9, 1/2 and 5/9, which is manifested in appearance of new magnetization plateaus on the magnetization curve of the model at given values of m/ms. The obtained results are consistent with experimental measurements of magnetization curves in selected rare-earth tetraborides.

A model for doping-dependent magnetic frustration and ordering in a triangular lattice

The family of cobaltates AxCoO2 (A = Na, Li, K), with a crystal structure consisting of a layered triangular lattice of Co ions, exhibits a fascinating range of coupled spin, charge and ion ordering phenomena as a function of electron doping content x. Based on these experimental observations, we investigate an extended Ising model for suppression of magnetic frustration caused by electron doping in a quasi–2-dimensional nearest-neighbour antiferromagnetic triangular lattice. As determined by geometry and bond-counting, it is found that magnetic frustration can be quantified by a frustration index fub and its magnitude is a non-monotonic function of x. A mean-field calculation is carried out to determine the temperature-dependent magnetization, spin-entropy and heat capacity for the obtained structures with the lowest energy (≡ lowest fub) for each x. The calculations reveal that the magnetic-ordering temperature TC exhibits an anti-correlation with fub as a function of x. In addition, as seen in thermopower experiments, an anomalous spin-entropy is obtained for the high-doping cases when . The results indicate the importance of doping-dependent magnetic frustration in the layered cobaltates.

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

We study ground state fidelity defined as the overlap between two ground states of the same quantum system obtained for slightly different values of the parameters of its Hamiltonian. We focus on the thermodynamic regime of the XY model and the neighborhood of its critical points. We describe in detail cases when fidelity is dominated by the universal contribution reflecting quantum criticality of the phase transition. We show that proximity to the multicritical point leads to anomalous scaling of fidelity. We also discuss fidelity in a regime characterized by pronounced oscillations resulting from the change of either the system size or the parameters of the Hamiltonian. Moreover, we show when fidelity is dominated by non-universal contributions, study fidelity in the extended Ising model, and illustrate how our results provide additional insight into dynamics of quantum phase transitions. Special attention is put to studies of fidelity from the momentum space perspective. All our main results are obtained analytically. They are in excellent agreement with numerics.

Ferrimagnetism Caused by Charge Ordering in Doped Antiferromagnetic Ising Spins

The emergence of ferrimagnetism caused by the charge ordering of commensurately doped charged Ising spins is proposed in the extended Ising model, equivalent to the Blume–Emery–Griffiths model. The stability of the ferrimagnetic state is discussed on the basis of the energy at zero temperature, the sublattice magnetizations from mean field approximation, and Monte Carlo simulation, as examples on triangular and square lattices. The magnitude of the ferrimagnetic moment is suggested in connection with the dimensionality of the lattice.

Simulation and Robustness Analysis for a Novel Capacitive/Magnetic Full-Turn Absolute Angular Position Sensor

In order to reduce the influence of axial displacement and/or to ease the assembly, certain capacitive angular sensors use symmetric designs limiting their absolute measuring range to (360/spl deg//n) where n is the number of blades. This paper presents a combined sensor that utilizes a Wiegand sensor to obtain additional information needed to resolve 360/spl deg/. Since magnetic and electric fields required by the sensing principles do not interfere, one single rotor design can be used for both fields. When the receiver coil on a Wiegand sensor has to drive a current, this current influences the shape and duration of the pulse generated by the sensor. We found that shape and amplitude of the pulse vary depending on the strength of the applied fields and the location of the initial inverse nucleation. Since most of design optimization for capacitive sensors is done by means of simulations, an adequate model of the combined sensor is needed. For the capacitive part, numerical approaches such as the finite element method are available. For the pulse wire part, an extended Ising model has been developed; results of measurements and numerical simulations are reported.

Multicriticality of the three-dimensional Ising model with plaquette interactions: an extension of Novotny's transfer-matrix formalism.

A three-dimensional Ising model with the plaquette-type (next-nearest-neighbor and four-spin) interactions is investigated numerically. This extended Ising model, the so-called gonihedric model, was introduced by Savvidy and Wegner as a discretized version of the interacting (closed) surfaces without surface tension. The gonihedric model is notorious for its slow relaxation to the thermal equilibrium (glassy behavior), which deteriorates the efficiency of the Monte Carlo sampling. We employ the transfer-matrix (TM) method, implementing Novotny's idea, which enables us to treat an arbitrary number of spins N for one TM slice even in three dimensions. This arbitrariness admits systematic finite-size-scaling analyses. Accepting the extended parameter space by Cirillo et al., we analyzed the (multi-) criticality of the gonihedric model for N</=13. Thereby, we found that, as first noted by Cirillo et al. analytically (cluster-variation method), the data are well described by the multicritical (crossover) scaling theory. That is, the previously reported nonstandard criticality for the gonihedric model is reconciled with a crossover exponent and the ordinary three-dimensional-Ising universality class. We estimate the crossover exponent and the correlation-length critical exponent at the multicritical point as phi=0.6(2) and nu; =0.45(15), respectively.

Domain Wall Migration in 3-d in the Presence of Diffusing Impurities

A new three-dimensional simulation procedure was developed for domain wall (grain boundary, APB, magnetic, etc.) migration in the presence of diffusing impurities. The simulation is based upon a kinetic Monte Carlo algorithm and an extended Ising model, incorporating both conserved and non-conserved dynamics. The simulations show a dependence of the domain wall velocity on driving force which is very similar to that seen in 2-d and in qualitative agreement with experiment. That is, the presence of a low mobility regime at small driving force and an abrupt transition to a high mobility regime at larger forces, under some conditions, and a continuous, non-linear dependence of the velocity on the force in others. The main qualitative difference between the 2-d and 3-d simulation results is in how the domain wall roughness depends on driving force. The velocity-driving force relation is not consistent with classic continuum models, but may be described, in the high velocity regime, by a theory based upon a discrete version of these models.

The phase diagram of cyclohexane–methanol: a challenge in chemical education

Cloud point and cooling curve studies of the cyclohexane–methanol system were ideally suited as a laboratory exercise for a physical chemistry curriculum. Within 3–4 h, students can obtain a sufficient number of relatively precise experimental data (temperature vs. mol fraction of methanol) to construct the major part of the solid–liquid phase diagram. The experimental procedure is based on three different methods: (1) cloud points were detected using an H–Ne laser; (2) temperatures of the methanol-rich part below the monotectic were taken when the first crystals of cyclohexane become visible; and (3) cooling curves were recorded in order to determine the melting point of C 6H 12 and the monotectic temperature. The results of the system exhibiting an upper critical solution temperature, UCST, agreed reasonably with the most reliable data presently available. Assuming a tetrameric methanol species, the experimental T− x data of the freezing-point depression and the sub-monotectic curve were fitted to a sub-regular model with three adjustable parameters for the liquid phase. However, only an extended Ising model agreed with the experimental curve near the critical temperature.