Next-nearest Neighbor Interactions Research Articles

The Hamiltonian three-parameter spaces of the q-state Potts model with three competing interactions on a Cayley tree

In this paper, we study the phase diagrams for the integer q-state (q ≥ 3) Potts model on a Cayley tree for order two with competing nearest-neighbor interactions J 1, prolonged next-nearestneighbor interactions J p and two-level triple-neighbor interactions J t . The exact phase diagrams of the Potts model with some competing interactions on a Cayley tree lattice of order two have been found. At vanishing temperature, the phase diagram is fully determined for all values and signs of J 1, J p and J t . Our aim is to generalize the results of Ganikhodjaev et al. to the q-state Potts model with competing nearest-neighbor, prolonged next-nearest-neighbor and two-level tripleneighbor interactions on a Cayley tree for order 2 and to compare these with previous results in the literature. Ganikhodjaev et al. reported on a new phase, denoted as a paramodulated (PM) phase, found at low temperatures and characterized by 2-periodic points of an one-dimensional dynamical system lying inside the modulated phase. An important note for such a phase is that inherently the Potts model has no analogues in the Ising setting. In this paper, we show that increasing the spin number from three (q = 3) to arbitrary q > 3 can dramatically affect the resultant phases (expanding the paramodulated phase). We believe that the enlarging of the paramodulated (PM) phase is essentially connected to the symmetry in the spin numbers.

Localization–delocalization transition of dipolar bosons in a four-well potential

We study interacting dipolar atomic bosons in a four-well potential within a ring geometry and outline how a four-site Bose–Hubbard (BH) model including next–nearest–neighbor interaction terms can be derived for the above four-well system. We analyze the ground state of dipolar bosons by varying the strength of the (effective) interaction between particles in next–nearest-neighbor wells. We perform this analysis both numerically and analytically by reformulating the dipolar-boson model within the continuous variable picture applied in Buonsante et al (2011 Phys. Rev. A 84 061601(R)). By using this approach we show that when the (effective) next-nearest–neighbor interaction crosses a precise value of the on-site interaction, the ground state exhibits a change from the uniform state (pertaining to the delocalization regime) to a macroscopic two-pulse state, with strongly localized bosons (localization regime). These predictions are confirmed by the results obtained by diagonalizing numerically the four-site extended BH Hamiltonian.

Monte Carlo investigation of the mixed spin Ising model with four-spin interaction and next-nearest neighbor couplings

A Monte Carlo method is used to investigate the phase diagram of the ferromagnetic two-dimensional mixed spin-1 and spin-1/2 Ising model with four-spin interaction J4 and next-nearest couplings J′. In the absence of this latter interaction, the system does not present any evidence for the tricritical point, whereas such behavior was suggested by finite cluster approximation. In the presence of the next-nearest neighbor interaction, the phase diagram is qualitatively and quantitatively different from that obtained with J′=0. It undergoes two kinds of behaviors according to the negative and positive value of J′. In particular, for J4/J2=−4 the system keeps the coexistence of the two ground states up to a J′-dependent finite temperature. In addition to the phase diagrams, the thermal dependence of the magnetizations have also been examined. Some characteristic features have been found which depend on the strengths of the interactions J4 and J′.

Quantization of [formula omitted]-Fermi–Pasta–Ulam lattice with nearest and next-nearest neighbor interactions

We quantize the β-Fermi–Pasta–Ulam (FPU) model with nearest and next-nearest neighbor interactions using a number conserving approximation and a numerically exact diagonalization method. Our numerical mean field bi-phonon spectrum shows excellent agreement with the analytic mean field results of Ivić and Tsironis (2006), except for the wave vector at the midpoint of the Brillouin zone. We then relax the mean field approximation and calculate the eigenvalue spectrum of the full Hamiltonian. We show the existence of multi-phonon bound states and analyze the properties of these states by varying the system parameters. From the calculation of the spatial correlation function we then show that these multi-phonon bound states are particle like states with finite spatial correlation. Accordingly we identify these multi-phonon bound states as the quantum equivalent of the breather solutions of the corresponding classical FPU model. The four-phonon spectrum of the system is then obtained and its properties are studied. We then generalize the study to an extended range interaction and consider the quantization of the β-FPU model with next-nearest-neighbor interactions. We analyze the effect of the next-nearest-neighbor interactions on the eigenvalue spectrum and the correlation functions of the system.

Edge modes in a frustrated quantum Ising chain

The ground state properties of an Ising chain with nearest ($J_{1}$) and next-nearest neighbor ($J_{2}$) interactions in a transverse field are investigated using the density matrix renormalization group and cluster mean-field theory methods. Its quantum phase diagram has two ordered regions (separated by a quantum disordered phase), one of which has simple ferromagnetic or N\'eel order depending upon the sign of $J_{1}$, and the other is the double-staggered antiferromagnetic phase. The presence of the Majorana-like edge-modes in these ordered phases is inferred by calculating the end-to-end spin-spin correlations on open chains. It is found that there occur four edge modes in the double-staggered phase, while the ferromagnetic and N\'eel phases support two edge modes, except very near $J_{1}=0$ where it seems they have four edge modes like the exact case at $J_{1}=0$ itself.

Anisotropic easy axis S=1 antiferromagnetic Heisenberg model with competitive interaction on a square lattice

Using a modified spin wave theory, we study the two-dimensional spin S=1 Heisenberg antiferromagnet with both spin and spatial anisotropies and competitive next-nearest neighbor interaction J2, at zero temperature. The magnetization as a function of J2 shows the existence of three different phases namely, ordered Néel, disordered and ordered collinear phases. The existence of the disordered phase depends on the values of the anisotropy parameters. The model shows a very rich phase diagram.

Frustrations and phase transitions in the Ising model on square lattice

The phase transitions in two-dimensional antiferromagnetic Ising model are studied on a square lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transition of second order and the frustration points depending on relative interaction values and magnetic field. A effect, heat capacity splitting near the frustration points, is found.

Phase Transitions in the Antiferromagnetic Heisenberg Model on a Triangular Lattice with the Next-Nearest Neighbor Interactions

The critical behavior and phase transitions (PT) of the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice with nearest-neighbor (J) and next-to-nearest neighbor (J1) interactions is studied by the replica Monte Carlo method. The first order phase transition has been revealed in the studied model based on the histogram method of processing data of the Monte Carlo for systems with large linear dimensions. Shown that the system exhibits the pseudouniversal critical behavior in the case of small lattices.

Frustrated three dimensional anisotropic antiferromagnet with single ion anisotropy

The SU(3) Schwinger bosons formalism is used to study the three dimensional anisotropic Heisenberg antiferromagnet with nearest and next-nearest neighbor interactions in the XY plane (and only nearest neighbor interactions along the z direction) and single ion anisotropy. The quantum phase transitions from the gapped disordered state to the ordered phases are studied. The phase diagram at zero temperature is calculated. We have two kinds of quantum phase transitions: one induced by the single-ion anisotropy term, and another caused by competitive interactions.

Towards photonic quantum simulation of ground states of frustrated Heisenberg spin systems

Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. Recent experiments have shown that photonic quantum systems have the advantage to exploit quantum interference for the quantum simulation of the ground state of Heisenberg spin systems. Here we experimentally characterize this quantum interference at a tuneable beam splitter and further investigate the measurement-induced interactions of a simulated four-spin system by comparing the entanglement dynamics using pairwise concurrence. We also study theoretically a four-site square lattice with next-nearest neighbor interactions and a six-site checkerboard lattice, which might be in reach of current technology.

Magnetic interactions in disordered perovskite PbFe1/2Nb1/2O3and related compounds: Dominance of nearest-neighbor interaction

We show that the magnetism of double perovskite AFe_{1/2}M_{1/2}O_3 systems may be described by the Heisenberg model on the simple cubic lattice, where only half of sites are occupied by localized magnetic moments. The nearest-neighbor interaction J_1 is more than 20 times the next-nearest neighbor interaction J_2, the third-nearest interaction along the space diagonal of the cube being negligible. We argue that the variety of magnetic properties observed in different systems is connected with the variety of chemical ordering in them. We analyze six possible types of the chemical ordering in 2x2x2 supercell, and argue that the probability to find them in a real compound does not correspond to a random occupation of lattice sites by magnetic ions. The exchange J_2 rather than J_1 define the magnetic energy scale of most double perovskite compounds that means the enhanced probability of 1:1 short range ordering. Two multiferroic compounds PbFe_{1/2}M_{1/2}O_3 (M=Nb, Ta) are exceptions. We show that the relatively high temperature of antiferromagnetic transition is compatible with a layered short-range chemical order, which was recently shown to be most stable for these two compounds [I. P. Raevski, {\em et al.}, Phys.\ Rev.\ B \textbf{85}, 224412 (2012)]. We show also that one of the types of ordering has ferrimagnetic ground state. The clusters with short-range order of this type may be responsible for a room-temperature superparamagnetism, and may form the cluster glass at low temperatures.

An Optimization-based Atomistic-to-Continuum Coupling Method

We present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the latter as a constrained optimization problem with virtual Dirichlet controls on the interfaces between the atomistic and continuum subdomains. The optimization objective is to minimize the error between the atomistic and continuum solutions on the overlap between the two subdomains, while the atomistic and continuum force balance equations provide the constraints. Separation, rather then blending of the atomistic and continuum problems, and their subsequent use as constraints in the optimization problem distinguishes our approach from the existing AtC formulations. We present and analyze the method in the context of a one-dimensional chain of atoms modeled using a linearized two-body potential with next-nearest neighbor interactions.

Magnetization plateaus in generalized Shastry-Sutherland models

We study an anisotropic Heisenberg antiferromagnet with ferromagnetic transverse spin exchange using exact quantum Monte Carlo methods. Such a model is relevant to a class of rare earth tetraboride materials that display a range of magnetization plateaus under applied magnetic field. The layered arrangement of magnetic ions in these materials is topologically equivalent to the Shastry-Sutherland lattice. In this frustrated geometry, we study the interplay of next-nearest neighbor interactions in stabilizing a plateau at half the saturation magnetization (or 1/2 plateau). We also show hysteresis-like behavior at the onset of the 1/3 plateau.

Incommensurate dynamic correlations in the quasi-two-dimensional spin liquid BiCu2PO6

We report detailed inelastic neutron scattering measurements on single crystals of the frustrated two-leg ladder BiCu2PO6, whose ground state is described as a spin liquid phase with no long-range order down to 6 K. Two branches of steeply dispersing long-lived spin excitations are observed with excitation gaps of \Delta_1 = 1.90(9) meV and \Delta_2 = 3.95(8) meV. Significant frustrating next-nearest neighbour interactions along the ladder leg drive the minimum of each excitation branch to incommensurate wavevectors \zeta_1 = 0.574\pi and \zeta_2 = 0.553\pi for the lower and upper energy branches respectively. The temperature dependence of the excitation spectrum near the gap energy is consistent with thermal activation into singly and doubly degenerate excited states. The observed magnetic excitation spectrum as well as earlier thermodynamic data could be consistently explained by the presence of strong anisotropic interactions in the ground state Hamiltonian.

Partial Order in Potts Models on the Generalized Decorated Square Lattice

We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-nearest (J2) neighbor interactions. Using the tensor renormalization-group method augmented by higher order singular value decompositions, we calculate the spontaneous magnetization of the Potts model with q = 2, 3, and 4. The results for q = 2 allow us to benchmark our numerics using the exact solution. For q = 3, we find a highly degenerate ground state with partial order on a single sublattice, but with vanishing entropy per site, and we obtain the phase diagram as a function of the ratio J2/J1. There is no finite-temperature transition for the q = 4 case when J1 = J2, whereas the magnetic susceptibility diverges as the temperature goes to zero, showing that the model is critical at T = 0.

Interacting steps with finite-range interactions: Analytical approximation and numerical results

We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions q on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

Self-Trapping in Discrete Nonlinear Schrödinger Equation with Next-Nearest Neighbor Interaction

The dynamical self-trapping of an excitation propagating on one-dimensional of different sizes with next-nearest neighbor (NNN) interaction is studied by means of an explicit fourth order symplectic integrator. Using localized initial conditions, the time-averaged occupation probability of the initial site is investigated which is a function of the degree of nonlinearity and the linear coupling strengths. The self-trapping transition occurs at larger values of the nonlinearity parameter as the NNN coupling strength of the lattice increases for fixed size. Furthermore, given NNN coupling strength, the self-trapping properties for different sizes are considered which are some different from the case with general nearest neighbor (NN) interaction.

Multibreather stability in discrete Klein–Gordon equations: Beyond nearest neighbor interactions

Abstract We present results on multibreather stability in one-dimensional nonlinear Klein–Gordon chains. Our analysis is based on Aubryʼs band theory and perturbation theory. First, we provide an alternative proof of the stability of multibreathers in a chain with nearest neighbor interactions only. Then, we extend our analysis to the case of interactions with up to three neighbors. For next-nearest neighbor and third-nearest neighbor interactions we also extend the theory to study the stability properties of recently found multibreathers that have nonstandard phase shifts (not equal to 0 or π).

Bilinear-biquadratic anisotropic Heisenberg model on a triangular lattice

Motivated by the fact that the study of disordered phases at zero temperature is of great interest, I study the spin-one quantum antiferromagnet with a next-nearest neighbor interaction on a triangular lattice with bilinear and biquadratic exchange interactions and a single ion anisotropy, using a SU(3) Schwinger boson mean-field theory. I calculate the critical properties, at zero temperature, for values of the single ion anisotropy parameter D above a critical value DC, where a quantum phase transition takes place from a higher D disordered phase to a lower D ordered phase.

Magnetic structure and magnon dispersion in LaSrFeO4

We present elastic and inelastic neutron scattering data on LaSrFeO$_4$. We confirm the known magnetic structure with the magnetic moments lying in the tetragonal basal plane, but contrarily to previous reports our macroscopic and neutron diffraction data do not reveal any additional magnetic phase transition connected to a spin reorientation or to a redistribution of two irreducible presentations. Our inelastic neutron scattering data reveals the magnon dispersion along the main-symmetry directions [0 $\xi$ 0] and [$\xi$ -$\xi$ 0]. The dispersion can be explained within linear spin-wave theory yielding an antiferromagnetic nearest-neighbour interaction parameter $J_{1}=7.4(1)$ meV and a next-nearest neighbour interaction parameter $J_{2}=0.4(1)$ meV. The dispersion is gapped with the out-of-plane anisotropy gap found at $\Delta_{out}=5.26(2)$ meV, while evidence is present that the in-plane anisotropy gap lies at lower energies, where it cannot be determined due to limited instrument resolution.