Random versus nonrandom competing bonds for spin glasses with long-range interactions

The mapping of random onto nonrandom competing bonds recently suggested is here implemented for spin glasses of long-ranged interactions. Exact results are obtained which support previous conclusions from high-temperature series.     

Anderson localization for radial tree-like random quantum graphs

We prove that certain random models associated with radial, tree-like, rooted quantum graphs exhibit Anderson localization at all energies. The two main examples are the random length model (RLM) and the random Kirchhoff model (RKM). In the RLM, the lengths of each generation of edges form a family of independent, identically distributed random variables (iid). For the RKM, the iid random variables are associated with each generation of vertices and moderate the current flow through the vertex. We consider extensions to various families of decorated graphs and prove stability of localization with respect to decoration. In particular, we prove Anderson localization for the random necklace model.     

Rigorous decimation-based construction of ground pure states for spin-glass models on random lattices

A constructive scheme for determining pure states at very low temperature in the 3-spins glass model on a random lattice is provided, in full agreement with Parisi's one step replica symmetry breaking (RSB) scheme. Proof is based on the analysis of a partial decimation procedure and of the statistical properties of its output, i.e., a reduced Hamiltonian acting on a subset of the initial spins. The number of ground states (GS) in each state, the number of states, and the distances between GS are calculated and correspond to RSB predictions.     

Effects of random biquadratic couplings in a spin-1 spin-glass model

A spin-1 model, appropriated to study the competition between bilinear (J _ij S _i S _j ) and biquadratic (K _ij S _i ² S _j ²) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins. Received 18 May 1999 and Received in final form 20 October 1999     

Ferromagnetic,spin-glass and paramagnetic phases in diluted heisenberg ferromagnet with fluctuating exchange bonds

We construct a simple CPA for studying ferromagnets which simultaneously possess site and (isotropic) exchange bond disorders. We use the theory to study spin-wave stiffness in diluted ferromagnet with exchange amorphousness and analyze the structure of the interfaces between ferromagnetic, spin-glass and paramagnetic phases of such a system.     

Anderson localization of expanding Bose-Einstein condensates in random potentials

We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length sigma(R). For speckle potentials the Fourier transform of the correlation function vanishes for momenta k>2/sigma(R) so that the Lyapunov exponent vanishes in the Born approximation for k>1/sigma(R). Then, for the initial healing length of the condensate xi(in)>sigma(R) the localization is exponential, and for xi(in)相似文献   

Rigorous mean-field model for coherent-potential approximation: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner'sn-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites, but free. Freeness of random variables is an analog of the concept of independence for noncommuting random operators. A possible realization is the ensemble of randomly rotated matrices at different lattice sites. The one- and two-particle Green functions of the proposed Hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is novanishing everywhere inside the band. The long-range behavior and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multisite) model is a rigorous mean-field model for the (single-site) CPA. We show how the Lloyd model is included in our model and treat various kinds of noises.     

Phase transitions in random Potts systems and the community detection problem: spin-glass type and dynamic perspectives

Phase transitions in spin-glass type systems and, more recently, in related computational problems have gained broad interest in disparate arenas. In the current work, we focus on the “community detection” problem when cast in terms of a general Potts spin-glass type problem. As such, our results apply to rather broad Potts spin-glass type systems. Community detection describes the general problem of partitioning a complex system involving many elements into optimally decoupled “communities” of such elements. We report on phase transitions between solvable and unsolvable regimes. A solvable region may further split into “easy” and “hard” phases. Spin-glass type phase transitions appear at both low and high temperatures (or noise). Low-temperature transitions correspond to an “order by disorder” type effect wherein fluctuations render the system ordered or solvable. Separate transitions appear at higher temperatures into a disordered (or an unsolvable) phase. Different sorts of randomness lead to disparate behaviors. We illustrate the spin glass character of both transitions and report on memory effects. We further relate Potts type spin systems to mechanical analogs and suggest how chaotic-type behavior in general thermodynamic systems can indeed naturally arise in hard computational problems and spin glasses. The correspondence between the two types of transitions (spin glass and dynamic) is likely to extend across a larger spectrum of spin-glass type systems and hard computational problems. We briefly discuss potential implications of these transitions in complex many-body physical systems.     

Phase diagram of the two-dimensional Ising model with random competing interactions

An Ising model with ferromagnetic nearest-neighbor interactions J₁ (J₁>0) and random next-nearest-neighbor interactions [+J₂ with probability p and −J₂ with probability (1−p); J₂>0] is studied within the framework of an effective-field theory based on the differential-operator technique. The order parameters are calculated, considering finite clusters with n=1,2, and 4 spins, using the standard approximation of neglecting correlations. A phase diagram is obtained in the plane temperature versus p, for the particular case J₁=J₂, showing both superantiferromagnetic (low p) and ferromagnetic (higher values of p) orderings at low temperatures.     

Anderson localization of a Bose-Einstein condensate in a 3D random potential

We study the effect of Anderson localization on the expansion of a Bose-Einstein condensate, released from a harmonic trap, in a 3D random potential. We use scaling arguments and the self-consistent theory of localization to show that the long-time behavior of the condensate density is controlled by a single parameter equal to the ratio of the mobility edge and the chemical potential of the condensate. We find that the two critical exponents of the localization transition determine the evolution of the condensate density in time and space.     

Suppression of Anderson localization in a graphene sheet applied by a random voltage pattern

We theoretically study the transport of electronic waves through a graphene sheet applied by a random voltage pattern in which the magnitudes and/or the widths of the voltages are random. When the magnitudes of the voltages exceed the electronic energy, the applied region can be considered as left-handed (LH) layers. Compared to the disordered structures with right-handed (RH) layers only, the spectra of the (average) density of states and the localization lengths in mixed random structures with RH and LH layers all show the suppression of Anderson localization, owing to the phase compensation effect of LH layers that reduces the long-range interference in the random system.     

Simulation of thermal decomposition of a polymer at random scissions of C-C bonds

A mathematical formulation of the polymer thermal decomposition model at random scissions of C-C bonds in the backbone is presented. The model is based on ideas about a macrokinetic character of the observed process Polymer ?? Gaseous products, and the thermofluctuation nature of the bond scission. The suggested approach makes it possible to calculate the decomposition rate in a wide pressure range at any initial molecular weight distribution of the polymer. As an example, a comparison of the calculation results for temperature-time dependences of the conversion degree and decomposition rate with experimental data obtained in isothermal and non-isothermal regimes is performed for linear polyethylene.