Ising-like Hamiltonian Research Articles

Static and dynamic properties of two-sublattice spin-crossover systems

We investigate the static and dynamic properties of spin-crossover systems in the presence of an external magnetic field using two-sublattice Ising-like Hamiltonian. At low temperatures both sublattices are in the LS state, and in the HS state at high temperatures. The new feature of spin-crossover is depicted for our model when we take the non-equivalent sublattices JA≠JB, the two-step spin-crossover phase transition is obtained with the presence of the hysteresis loop. In order to study the properties of two-step spin-crossover, we use the lowest approximation of the cluster variation method for static properties. The dynamic properties of the system with bilinear interactions are studied by the path probability method. We present high-spin state fraction nHS vs temperature and magnetic field variations for constant values of the degeneracy ratio between high-spin and low-spin states. In the present model, we obtained the relaxation curves of the order parameters SA and SB using different temperature values. Finally, the flow diagram of the order parameters is depicted for different values of rate constant k1 and temperature, which displays the stable, metastable, and unstable properties. Static and dynamic self-consistent equations of the system were performed by using Newton-Raphson and Runge-Kutta methods.

Optimizing radiotherapy plans for cancer treatment with Tensor Networks

We present a novel application of Tensor Network methods in cancer treatment as a potential tool to solve the dose optimization problem in radiotherapy. In particular, the intensity-modulated radiation therapy technique—that allows treating irregular and inhomogeneous tumors while reducing the radiation toxicity on healthy organs—is based on the optimization problem of the beamlets intensities that shall result in a maximal delivery of the therapy dose to cancer while avoiding the organs at risk of being damaged by the radiation. The resulting optimization problem is expressed as a cost function to be optimized. Here, we map the cost function into an Ising-like Hamiltonian, describing a system of long-range interacting qubits. Finally, we solve the dose optimization problem by finding the ground-state of the Hamiltonian using a Tree Tensor Network algorithm. In particular, we present an anatomical scenario exemplifying a prostate cancer treatment. A similar approach can be applied to future hybrid classical–quantum algorithms, paving the way for the use of quantum technologies in future medical treatments.

A First Order Phase Transition Studied by an Ising-Like Model Solved by Entropic Sampling Monte Carlo Method

Two-dimensional (2D) square, rectangular and hexagonal lattices and 3D parallelepipedic lattices of spin crossover (SCO) compounds which represent typical examples of first order phase transitions compounds are studied in terms of their size, shape and model through an Ising-like Hamiltonian in which the fictitious spin states are coupled via the respective short and long-range interaction parameters J, and G. Furthermore, an environmental L parameter accounting for surface effects is also introduced. The wealth of SCO transition properties between its bi-stable low spin (LS) and high spin (HS) states are simulated using Monte Carlo Entropic Sampling (MCES) method which favors the scanning of macro states of weak probability occurrences. For given J and G, the focus is on surface effects through parameter L. It is shown that the combined first-order phase transition effects of the parameters of the Hamiltonian can be highlighted through two typical temperatures, TO.D., the critical order-disorder temperature and Teq the equilibrium temperature that is fixed at zero effective ligand field. The relative positions of TO.D. and Teq control the nature of the transition and mediate the width and position of the thermal hysteresis curves with size and shape. When surface effects are negligible (L = 0), the equilibrium transition temperature, Teq. becomes constant, while the thermal hysteresis’ width increases with size. When surface effects are considered, L ≠ 0, Teq. increases with size and the first order transition vanishes in favor of a gradual transition until reaching a threshold size, below which a reentrance phenomenon occurs and the thermal hysteresis reappears again, as shown for hexagonal configuration.

Optimization of quantum computing models inspired by D-wave quantum annealing

With the slow progress of universal quantum computers, studies on the feasibility of optimization by a dedicated and quantum-annealing-based annealer are important. The quantum principle is expected to utilize the quantum tunneling effects to find the optimal solutions for the exponential-level problems while classical annealing may be affected by the initializations. This study constructs a new Quantum-Inspired Annealing (QIA) framework to explore the potentials of quantum annealing for solving Ising model with comparisons to the classical one. Through various configurations of the 1D Ising model, the new framework can achieve ground state, corresponding to the optimum of classical problems, with higher probability up to 28% versus classical counterpart (22% in case). This condition not only reveals the potential of quantum annealing for solving the Ising-like Hamiltonian, but also contributes to an improved understanding and use of the quantum annealer for various applications in the future.

Statistical model for nanoparticles formation: Self-consistent field approximation

In this paper, we propose a statistical model for the formation of metal nanoparticles in a homogeneous infinite medium. The Ising-like Hamiltonian of a system is analysed using the self-consistent field approximation for the lattice-gas model. Exclusively direct atom–atom interactions are considered. A special role of surface atoms and their interaction with the external medium are discussed in detail. The grand thermodynamic potential of a system is calculated and other thermodynamic functions are obtained. A consistent set of equations is found for describing both the radii of nanoparticles and their density (occupation number). The essential role of the medium nonhomogeneity in the process of nanoparticles arising is proved. The temperature dependence for the radii of the formed gold nanoparticles is estimated and the variance of their sizes is calculated.

Analysis of Architecture Effect on Hysteretic Behavior of 3-D Spin Crossover Nanostructures

We have analyzed the hysteretic properties of thermal and pressure induced low spin (LS)↔high spin (HS) phase transition of a 3-D spin crossover (SCO) nanostructure when the cluster architecture is progressively changed from a cubic to a thin film. For solving the 3-D Ising-like Hamiltonian, the Monte Carlo metropolis technique is used, with the edge molecules trapped in HS state. The role of short- and long-range interactions on the SCO cooperativity has been investigated as well. The obtained results show that the cooperativity of a 3-D SCO system, characterized by the same number of molecules and the same interactions strength are strongly affected when going from a cubic 3-D to thin-film architecture. These results are discussed in terms of surface effects.

Free energy functional of the Ising-like model of spin crossover

The model of spin crossover based on the Ising-like Hamiltonian (IHM) has been analysed by deriving the functional of free energy from the mean-field solutions of this Hamiltonian. The contribution of the configurational entropy was found to be identical to that in the functional of the molecular statistical model (MSM) of spin crossover. However, the polynomial expansion over composition (x B) and degree of order (s B) in these functionals differ fundamentally due to different ways of accounting for the effects of molecular interactions. It was found that IHM takes into account next-to-nearest neighbour interactions by introducing affinities of sublattices towards molecules of given kinds. This yields a term proportional to the first power of the degree of order in the functional of IHM, whereas the MSM free energy is only proportional to s B 2 . The choice of formal independent variables does not affect the results of simulations of transition curves provided the functional remains unaltered. This provides for more flexibility in numerical simulations of transition curves.

Magnetic anisotropy in the octanuclear [formula omitted] cluster exhibiting Single-Molecule Magnet behavior: Quantum-spin and classical-spin approaches

A theoretical model is developed for the explanation of the magnetic properties of the [MnCl] 4[Re(triphos)(CN) 3] 4 single molecule magnet, which represents a 3d–5d molecular cube compressed along one of the C 3 axes. In the model, the strong local trigonal crystal field on each Re(II) ion is assumed to split the ground cubic 2 T 2( t 2 5 ) term into the states 2 A 1 and 2 E in such a way that 2 E term proves to be the ground one. The ground Kramers doublet that appears under the spin–orbit splitting of the 2 E term is shown to be fully anisotropic ( g ⊥ = 0) and the magnetic superexchange (mediated by cyanide bridge) between Re and Mn ions is approximated by the Ising-like Hamiltonian. In this case, the magnetic anisotropy of the trigonally distorted cube represents a first order effect that is totally incorporated in the effective Ising-like Hamiltonian, including the pseudo-spin-1/2 operator for the Re(II) ion and the operator of the true spin-5/2 for the Mn(II) ion. The developed pseudo-spin-1/2 formalism is applied to the explanation of the DC magnetic susceptibility and magnetization data, and the set of the best fit parameters is found. The temperature dependence of the DC magnetic susceptibility and the field dependence of the magnetization calculated with this set of parameters are in accord with the experimental data being at the same time compatible with the existence of the barrier for magnetization reversal. Finally, the applicability of the quantum–classical spin approach for the calculation of the magnetic properties of large 3d–5d clusters is discussed.

Classical Ising chain in transverse field

The spin 1 2 Ising chain in transverse field is considered the prototypical system for quantum phase transitions. However, very little is apparently known in literature about its classical counterpart, not to be confused with the standard classical Ising model: while the latter is constructed from classical discrete variables, the model we consider is a chain of classical vectors of modulus 1, interacting via an Ising-like Hamiltonian. When an uniform field is applied perpendicular to the exchange interaction, both the quantum model and its classical counterpart get to be characterized by a critical field separating a ferromagnetically ordered state of minimal energy from a paramagnetic one. The properties of the classical model, and especially the behaviour of the correlation length, are investigated at low temperature around the critical field and compared with those of the quantum model, in order to single out the role played by quantum and classical fluctuations at finite temperature; the possibility to experimentally observe peculiar quantum critical effects in Ising spin chains is discussed.

Dynamical Ising-like model for the two-step spin-crossover systems

In order to reproduce the two-step relaxation observed experimentally in spin-crossover systems, we investigate analytically the static and the dynamic properties of a two-sublattice Ising-like Hamiltonian. The formalism is based on a stochastic master equation approach. It is solved in the mean-field approximation, and yields two coupled differential equations that correspond to the HS fractions of the sublattices A and B.

Superlattice energetics and alloy thermodynamics of GaAs/Ge

We re-examine the validity of the three-dimensional bulk thermodynamic description for the zinc-blende-to-diamond transition observed in ( GaAs) 1− x Ge 2 x alloys. We use interaction parameters extracted from first-principles local-density total-energy calculations for ( GaAs) p /( Ge 2) p superlattices and a cluster-variation solution to the corresponding Ising-like hamiltonian. The resulting phase diagram obtained with such a realistic energy model fails to account for the observed critical composition in the relevant temperature range, suggesting that, contrary to a previous view, the transition is not driven by bulk thermodynamics.

Model for the order-disorder transition in YBa2Cu

We present a model for the tetragonal-to-orthorhombic structural phase transition in YBa/sub 2/Cu/sub 3/O/sub y/. We assume the transition involves only the oxygen atoms which form the Cu-O chains in this compound and use an Ising-like Hamiltonian on a square lattice with nearest- and next-nearest-neighbor interactions to describe the system. Comparison of theoretical predictions with experimental results for site occupancy as a function of temperature and oxygen partial pressure shows good agreement.

The singlet-triplet Ising model. I. Application to simple fluids, nematic mixtures and3He-4He mixtures

A four-state lattice gas model is introduced in order to simulate the thermodynamical behaviour of simple fluids, nematic mixtures, and 3He-4He mixtures at variable pressure. The Ising-like Hamiltonian is treated in the molecular field approximation and various experimental phase diagrams are reproduced.

Double spin one-half lattice gas model

Abstract A double spin one-half lattice gas model is introduced in order to describe a magnetic annealed binary alloy or a nematic mixture. The Ising-like hamiltonian is solved in the molecular field approximation. Various phase diagrams are found, exhibiting unmixing critical points, magnetic critical lines, triple and tricritical points.

Spin-1 lattice-gas model. II. Condensation and phase separation in a binary fluid

A spin-1 lattice-gas model is shown to describe condensation and phase separation in a binary fluid. The Ising-like Hamiltonian involves quadrupolar, dipolar, and crossed quadrupolar-dipolar interactions and is treated in the molecular-field approximation. Various experimental phase diagrams are reproduced qualitatively, exhibiting liquid-gas and liquid-liquid equilibrium lines, critical, azeotropic, and triple lines.

Spin-1 lattice-gas model. I. Condensation and solidification of a simple fluid

A spin-1 lattice-gas model, similar to the Blume-Emery-Griffiths model for $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ mixtures, is shown to describe condensation and solidification of a simple fluid. The Ising-like Hamiltonian of the system involves quadrupolar and dipolar interactions, which are responsible for condensation and solidification, respectively. The molecular-field approximation is used, and the ordinary phase diagram of a simple fluid is reproduced. However, for some range of the parameters, the liquid-gas equilibrium curve disappears. Also, the melting curve may exhibit a tricritical point: For pressures larger than the tricritical pressure, critical melting is found. Other physical applications of the model are briefly discussed.