Next-nearest Neighbour Ising Model Research Articles

Supervised training of neural-network quantum states for the next-nearest neighbor Ising model

Different neural network architectures can be unsupervisedly or supervisedly trained to represent quantum states. We explore and compare different strategies for the supervised training of feed forward neural network quantum states. We empirically and comparatively evaluate the performance of feed forward neural network quantum states in different phases of matter for variants of the architecture, for different hyper-parameters, and for two different loss functions, to which we refer as mean-squared error and overlap, respectively. We consider the next-nearest neighbor Ising model for the diversity of its phases and focus on its paramagnetic, ferromagnetic, and pair-antiferromagnetic phases. We observe that the overlap loss function allows better training of the model across all phases, provided a rescaling of the neural network.

Counterdiabatic optimized driving in quantum phase sensitive models

State preparation plays a pivotal role in numerous quantum algorithms, including quantum phase estimation. This paper extends and benchmarks counterdiabatic driving protocols across three one-dimensional spin systems characterized by phase transitions: the axial next-nearest neighbor Ising, XXZ, and Haldane–Shastry models. We perform a shallow quantum optimal control over the counterdiabatic protocols by optimizing an energy cost function. Moreover, we provide a code package for computing symbolically various adiabatic gauge potentials. This protocol consistently surpasses standard annealing schedules, often achieving performance improvements of several orders of magnitude. The axial next-nearest neighbor Ising model stands out as a notable example, where fidelities exceeding 0.5 are attainable in most cases. Furthermore, the optimized paths exhibit promising generalization capabilities to higher-dimensional systems, allowing for the extension of parameters from smaller models. Nevertheless, our investigations reveal limitations in the case of the XXZ and Haldane–Shastry models, particularly when transitioning away from the ferromagnetic phase. This suggests that finding optimal diabatic gauge potentials for specific systems remains an important research direction.

Effect of Substrate on One-Dimensional Multiferroic Properties

We present a theoretical study of the substrate influence on the electrical and magnetic properties of a one-dimensional multiferroic. We used a one-dimensional axial next-nearest neighbor Ising model (1D ANNNI model). The effect of the substrate was modeled using the periodic Frenkel–Kontorova potential. It is shown that the periodic potential of the substrate reduces the polarization of the multiferroic at low temperatures. The substrate potential significantly affects the structural changes near the magnetic phase transition temperature.

Erratum: Calculation of the Stacking Fault Energy by Using the Anisotropic Next-Nearest Neighbor Ising Model

Erratum: Calculation of the Stacking Fault Energy by Using the Anisotropic Next-Nearest Neighbor Ising Model

Calculation of the Stacking Fault Energy by Using the Anisotropic Next-Nearest Neighbor Ising Model

Calculation of the Stacking Fault Energy by Using the Anisotropic Next-Nearest Neighbor Ising Model

Study of the Two-Dimensional Anisotropic Ising Model with Competing Interactions in the Region of a Transition from the Ferromagnetic to Paramagnetic State

The two-dimensional anisotropic Ising model with competing interactions in the region of a transition from the ferromagnetic to paramagnetic phase has been studied by the Monte Carlo method using the Wang–Landau algorithm. State density distributions have been obtained and the order parameters corresponding to different energies have been calculated. The temperature dependences of the thermodynamic parameters including the internal energy, magnetization, free energy, entropy, specific heat at constant magnetization, and Binder cumulants have been calculated. Using the Binder cumulant method and histogram analysis, it has been shown that a single second-order phase transition from the ferromagnetic to paramagnetic phase occurs at two exchange coupling constants ratios |J1/J| = 0.1 and 0.2 in the two-dimensional anisotropic next-nearest neighbor Ising model. The phase transition temperatures have been calculated. The main critical exponents have been determined using the finite-size scaling theory.

3D ISING NONUNIVERSALITY: A MONTE CARLO STUDY

We investigate as a member of the Ising universality class the Next-Nearest Neighbor Ising model without external field on a simple cubic lattice by using the Monte Carlo Metropolis Algorithm. The Binder cumulant and the susceptibility ratio, which should be universal quantities at the critical point, were shown to vary for small negative next-nearest neighbor interactions.

Ab initio determination of the (001) antiphase-boundary energy in the D022 Ni3V compound

Abstract The cohesive energies of L12, D022, D023 and selected one-dimensional (1D) long-period structures (LPSs) based on the L12 structure in the Ni-V system for the Ni3V composition have been obtained by ab-initio calculations using the Vienna ab-initio simulation package. Relaxations, both external and internal with respect to the cell, are taken into account in the determination of the structural stability of the 1D LPSs. At each stage of the relaxation process the D022 structure is the ground state. The values of the (001) antiphase-boundary (APB) energies are obtained from the energy differences of 1D LPSs with respect to either L12 or D022, with stacking of at least three L12 cubes along the direction perpendicular to the APB. The energy effects in the 1D LPSs are described in the framework of an axial next-nearest neighbour Ising model. The values of the interaction parameters are obtained in the ideal, distorted and fully relaxed structures. The APB energies are also derived from these parameter...

Field-induced phase transitions in an antiferroelectric liquid crystal using the pyroelectric effect

The antiferroelectric liquid crystal (AFLC) under investigation possesses different helical polar phases. Measurements of pyroelectric response of these phases as a function of temperature and bias field have elucidated the ability of this method for investigating the nature of antiferroelectric phases and phase transitions under the bias field. The pyroelectric signal as a function of the bias field at fixed temperatures and as a function of temperature for fixed bias fields was measured for different phases of the investigated AFLC material. A theoretical model describing the pyroelectric response in different phases of AFLC is given, and the experimental results are interpreted. The threshold fields for field induced phase transitions are determined. The type of field induced phase transition from the AF phase in particular is found to be dependent on the temperature within its range. The properties of an unusual ferrielectric phase existing between ferrielectric chiral smectic-C (SmC*) and antiferroelectric AF phases are studied in a great detail. The results confirm that this phase is one of the incommensurate phases, predicted by the axial next-nearest neighbor Ising model and Landau model for this temperature region.

Commensurate and incommensurate phases on Si(001) and Ge(001) surfaces

A model for the Si(001) and Ge(001) surface reconstruction is proposed on the basis of the next-nearest neighbour Ising model. The phase transitions (2 × 1) → c(4 × 2) and (2 × 1) → incommensurate phase → c(4 × 2) are investigated. The problem is solved in the vicinity of the Lifshitz point. The systems incommensurate along one and two directions are considered. A state diagram is obtained. The changes of the phase transition temperature under the action of hydrostatic pressure are discussed. The energetic parameters of the model are estimated for Si(001) and Ge(001).

Phenomenological renormalisation of Monte Carlo data

A method, akin to phenomenological renormalisation, for analysing Monte Carlo data in the critical region is proposed. The method is illustrated by an analysis of the structure factor of the two-dimensional axial next-nearest neighbour Ising model.

Low temperature analysis of the axial next-nearest neighbour Ising model near its multiphase point

The general, axial next-nearest neighbour Ising (or ANNI) model inddimensions consists of (d— 1)-dimensional layers of spins, si= + 1, with nearest-neighbour ferromagnetic coupling, J0> 0, within layers but competing ferromagnetic, and antiferromagnetic,J2< 0, first- and second-neighbour axial coupling between layers. By systematic low temperature expansions in powers of e-2Jo/kBT, extended to all orders where necessary, it is shown ford> 2 that in the vicinity of amultiphasepoint atT= 0 and k = —J2/J1= 1/2 there occurs an infinite sequence of distinct, commensurate modulated phases characterized by wavevectors + l)< z for j = 0, 1, 2, .... The phase boundaries, kj(T), and corresponding free energies and interfacial tensions are derived explicitly for low temperatures.

An infinity of commensurate phases in a simple Ising system: The ANNNI model (invited)

The ANNNI or axial next-nearest neighbor Ising model in d dimensions consists of (d−1)-dimensional layers of Ising spins, si = ±1, with nearest neighbor ferromagnetic couplings, J0≳0, within layers but competing ferromagnetic, J1, and antiferromagnetic, J2 = −κJ1<0, axial couplings between spins in first- and second-neighboring layers. It is the simplest model expected to display spatially modulated magnetically ordered states with wavevectors nontrivially related to the lattice spacing a, as observed in various real systems. The ground state is ferromagnetic for κ<1/2; of (2, 2), or 〈2〉, antiphase character (two layers ’’up’’, two ’’down’’, periodically) for κ≳1/2; but infinitely degenerate for κ = 1/2. Systematic low-temperature expansions may be generated about all possible ground states and carried to all orders where necessary. For d≳2 they show that (T,κ) = (0,1/2) is a multiphase point from which spring an infinite sequence of distinct, spatially modulated commensurate phases, 〈2j−13〉, with wavevectors q̄ = πj/(2j+1)a for j = 1,2, ⋅⋅⋅ . The free energy, phase boundaries, and corresponding domain wall energies can be given explicitly at low temperatures. On approaching the ’’melting’’ line, κ∞(T), of the 〈2〉 phase the wavevector varies quasicontinuously as 1/‖1n[κ∞(T)−κ]‖, displaying a ’’devil’s top step’’ just as the 〈2〉 phase locks in.