Order and disorder lines in systems with competing interactions: I. Quantum spins atT=0

In the parameter space of systems with competing interactions there are specific trajectories called order (disorder) lines. Along these trajectories the competition between the different interactions effectively reduces the dimensionality of the system and the model can be exactly solved. It is shown that the order (disorder) trajectories end up at a multicritical point. The method of Peschel and Emery is used to determine the (anisotropic) critical behavior of the spin-spin correlation functions near the multicritical point. The quantum spin systems discussed here include theXYZ chain in a field, the straggeredXYZ chain in a field, and a Hamiltonian version of a three-dimensional Ising model with biaxial competing interactions.On leave from and address after September 1, 1982: Institute for Theoretical Physics, Eötvös University, Puskin U. 5-7, 1088 Budapest, Hungary.     

Coupled fractional nonlinear differential equations and exact Jacobian elliptic solutions for exciton–phonon dynamics

An improved quantum model for exciton–phonon dynamics in an α-helix is investigated taking into account the interspine coupling and the influence of power-law long-range exciton–exciton interactions. Having constructed the model Hamiltonian, we derive the lattice equations and employ the Fourier transforms to go in continuum space showing that the long-range interactions (LRI) lead to a nonlocal integral term in the equations of motion. Indeed, the non-locality originating from the LRI results in the dynamic equations with space derivatives of fractional order. New theoretical frameworks are derived, such that: fractional generalization of coupled Zakharov equations, coupled nonlinear fractional Schrödinger equations, coupled fractional Ginzburg–Landau equations, coupled Hilbert–Zakharov equations, coupled nonlinear Hilbert–Ginzburg–Landau equations, coupled nonlinear Schrödinger equations and coupled nonlinear Hilbert–Schrödinger equations. Through the F-expansion method, we derive a set of exact Jacobian solutions of coupled nonlinear Schrödinger equations. These solutions include Jacobian periodic solutions as well as bright and dark soliton which are important in the process of energy transport in the molecule. We also discuss of the impact of LRI on the energy transport in the molecule.     

Note on the two-slit experiment

According to the general philosophy of quantum mechanics, a particle whose passage through one of the slits of a two-slit apparatus has been detected does not produce interference. In a previous article this was demonstrated explicitly by solving the Schrödinger equation for a specific model of the detector, but only the first order in the interaction with the detector was considered. In the present note it is shown for the same model that for stronger interactions the interference disappears altogether. When the detector has reached 100% efficiency those particles that have not been detected do not produce interference either, because they are sure to have passed through the other slit.For Oliver Penrose, as a token of esteem.     

Renormalization group approach to three-state spin models in two dimensions

The real space renormalization group approach is used to study spin one anisotropic models with dipolar and quadrupolar interactions on the triangular lattice. The method is tested for the three state Potts model and the Blume-Emery-Griffiths model leading to results which are basically in agreement with other treatments of these models. The phase diagram for a quadrupolar model (anisotropic Potts model) is obtained and the influence of an external magnetic field on the transition temperature to the quadrupolar phase is determined. The fixed point which controls a transition to the phase with Ising dipolar order andXY-type quadrupolar order is found.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Perturbation expansion for a one-dimensional Anderson model with off-diagonal disorder

The weak disorder expansion for a random Schrödinger equation with off-diagonal disorder in one dimension is studied. The invariant measure, the density of states, and the Lyapunov exponent are computed. The most interesting feature in this model appears at the band center, where the differentiated density of states diverges, while the Lyapunov exponent vanishes. The invariant measure approaches an atomic measure concentrated on zero and infinity. The results extend previous work of Markos to all orders of perturbation theory.     

Simulation of two and three-dimensional disordered systems: Lifshitz tails and localization properties

Very large two and three-dimensional realizations of the Anderson model for localization are studied by solving the time-dependent Schrödinger equation. The density of states is calculated and Lifshitz tails extracted. Eigenstates at various energies are computed and analyzed. The localization length is determined as a function of the strength of the disorder and energy. For moderate disorder substantial deviations from results obtained by the strip-and-rod technique are found.     

Anderson localization for Bernoulli and other singular potentials

We prove exponential localization in the Anderson model under very weak assumptions on the potential distribution. In one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment. In particular this solves the longstanding problem of localization for Bernoulli potentials (i.e., potentials that take only two values). In dimensions greater than one we prove localization at high disorder for potentials with Hölder continuous distributions and for bounded potentials whose distribution is a convex combination of a Hölder continuous distribution with high disorder and an arbitrary distribution. These include potentials with singular distributions.We also show that for certain Bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component.Partially supported by NSF grant DMS 85-03695Partially supported by NSF grant DMS 83-01889Partially supported by G.N.F.M. C.N.R.     

Determination of hyperfine fields from perturbed angular distributions of Mössbauer scattered radiation

Measurements of the angular distribution of Mössbauer scattering are known to be a powerful tool for the determination of small hyperfine fields. This method, however, is complicated by a systematic error due to Rayleigh scattering. It is shown how the measured data can be corrected for this disturbing contribution in order to obtain reliable results. The usefulness of this method is illustrated by applying it to the problem of the Mössbauer line broadening in stainless steel samples. Quadrupole interactions are found to be the main causes for this broadening.     

Localization for off-diagonal disorder and for continuous Schrödinger operators

We extend the proof of localization by Delyon, Lévy, and Souillard to accommodate the Anderson model with off-diagonal disorder and the continuous Schrödinger equation with a random potential.Work supported in part by Nato under Nato Grant # 346/84Research partially supported by USNSF under grant DMS 84-16049     

Effect of interactions, disorder and magnetic field in the Hubbard model in two dimensions

The effects of both interactions and Zeeman magnetic field in disordered electronic systems are explored in the Hubbard model on a square lattice. We investigate the thermodynamic (density, magnetization, density of states) and transport (conductivity) properties using determinantal quantum Monte Carlo and inhomogeneous Hartree Fock techniques. We find that at half filling there is a novel metallic phase at intermediate disorder that is sandwiched between a Mott insulator and an Anderson insulator. The metallic phase is highly inhomogeneous and coexists with antiferromagnetic long-range order. At quarter filling also the combined effects of disorder and interactions produce a conducting state which can be destroyed by applying a Zeeman field, resulting in a magnetic field-driven transition. We discuss the implication of our results for experiments.     

About a collective state for H-atoms in a hydrogen bonded chain

The possibility of having a collective state for the H-atoms in a hydrogen bonded chain is studied. In the specific case of HF the many body interactions between H-atoms are considered. The possibility of order—disorder phenomena is then suggested on the basis of an exactly solvable model.     

Divide and conquer: resonance induced by competitive interactions

We study an Ising model in a network with disorder induced by the presence of both attractive and repulsive links and subjected to a periodic subthreshold signal. By means of numerical simulations and analytical calculations we give evidence that the global response of the system reaches a maximum value for a given fraction of the number of repulsive interactions. The model can represent a network of spin-like neurons with excitatory and inhibitory couplings, or a simple opinion spreading model. In this context, attractive/repulsive links represent friends and enemies. “Divide and Conquer” refers to the fact that in order to force a society to adopt a new point of view, it helps to break its homogeneity by fostering enmities amongst its members.     

Coherence of Disordered Bosonic Gas with Two-and Three-Body Interactions

We theoretically and numerically investigate the coherence of disordered bosonic gas with effective two-and three-body interactions within a two-site Bose-Hubbard model.By properly adjusting the two-and three-body interactions and the disorder,the coherence of the system exhibits new and interesting phenomena,including the resonance character of coherence against the disorder in the purely two-or three-body interactions system.More interestingly,the disorder and three-body interactions together can suppress the coherence of the purely three-body interactions system,which is different from the case in which the disorder and two-body interactions together can enhance the coherence in certain values of two-body interaction.Furthermore,when two-or threebody interactions are attractive or repulsive,the phase coherence exhibits completely different phenomena.In particular,if two-or three-body interactions are attractive,the coherence of the system can be significantly enhanced in certain regions.Correspondingly,the phase coherence of the system is strongly related to the effective interaction energy.The results provide a possible way for studying the coherence of bosonic gas with multi-atoms' interactions in the presence of the disorder.     

Infrared spectra of hydrogen impurities in BaTiO3 crystals

The IR spectra in the 2.8 μm region of the OH^? impurities in thick single domain crystals have been measured for different polarization geometries and various temperatures. Simple calculations of the Coulomb interactions between hydrogen and lattice ions show that these interactions are much more important than the hydrogen bonding ones for determining the positions of the hydrogen ions. The appearance of only one strong non-dichroic OH^? stretching line is due to an almost equal population of the proton axial sites. The side bands are interpreted as combinations of the stretching mode with a low-frequency translational mode. The large broadening of the main line just above T_c supports the model which attributes a considerable order—disorder character to the ferroelectric phase transition.     

Spin- and charge density perturbations and short-range order in Fe–Cu and Fe–Zn BCC alloys: A Mössbauer study

A model used to describe the ⁵⁷Fe Mössbauer spectra for the binary BCC iron alloys rich in iron has been extended to account for the alloy crystallographic ordering. The ordering is accounted for by introducing single order parameter. Extension of the model is described in detail. The model has been tested applying it to the Fe–Cu alloys obtained by the arc melting and to the Fe–Zn alloys prepared by the solid state reaction. Random alloys are obtained up to ∼2 at% of Cu, and up to ∼8 at% of Zn. For higher impurity (minor alloy component) concentration it has been found that Cu atoms try to avoid Fe atoms in the iron matrix as nearest neighbors, while the opposite happens to the Zn atoms, albeit at much lesser scale, i.e., Zn–Zn interactions are much weaker than Fe–Zn interactions at the nearest neighbor distance. Perturbations to the iron magnetic hyperfine field (spin density) and electron (charge) density on the iron nucleus have been obtained for both series of alloys versus impurity concentration.     

Mössbauer study of defects created by low-fluence In+ implantations in InP

The temperature and fluence dependence of defect interactions in damage cascades in n-type InP has been investigated with ion-implanted radioactive¹¹⁹In (T _1.2=2.1 min) probe atoms. The hyperfine interactions for the¹¹⁹Sn Mössbauer daughter atoms in the resulting defect structures have been determined. An annealing model based on the temperature dependent mobility of lattice defects and their interactions in three observed annealing stages is proposed.     

Model for domain wall avalanches in ferromagnetic thin films

The Barkhausen jumps or avalanches in magnetic domain-walls motion between successive pinned configurations, due the competition among magnetic external driving force and substrum quenched disorder, appear in bulk materials and thin films. We introduce a model based in rules for the domain wall evolution of ferromagnetic media with exchange or short-range interactions, that include disorder and driving force effects. We simulate in 2-dimensions with Monte Carlo dynamics, calculate numerically distributions of sizes and durations of the jumps and find power-law critical behavior. The avalanche-size exponent is in excellent agreement with experimental results for thin films and is close to predictions of the other models, such as like random-field and random-bond disorder, or functional renormalization group. The model allows us to review current issues in the study of avalanches motion of the magnetic domain walls in thin films with ferromagnetic interactions and opens a new approach to describe these materials with dipolar or long-range interactions.     

New multiple histogram method for studying phase transitions

For temperature zero the effects of disorder for interacting bosons are considered. The disorder induced superfluid-insulator transition in thed-dimensional disordered Bogoliubov model is discussed. Results for a short-range and a long-range random potential are given. For short-range disorder we argue that ford<4 arbitrarily small disorder localizes the Bose condensate for vanishing interaction potential. Ford>4 a certain strength of the disorder potential is necessary in order to localize the condensate. For the three-dimensional Bogoliubov model our results are in agreement with a recent calculation. We compare our theoretical predictions with numerical experiments for a disordered boson Hubbard model.