First-order transition in a three-dimensional disordered system

We present the first detailed numerical study in three dimensions of a first-order phase transition that remains first order in the presence of quenched disorder (specifically, the ferromagnetic-paramagnetic transition of the site-diluted four states Potts model). A tricritical point, which lies surprisingly near the pure-system limit and is studied by means of finite-size scaling, separates the first-order and second-order parts of the critical line. This investigation has been made possible by a new definition of the disorder average that avoids the diverging-variance probability distributions that plague the standard approach. Entropy, rather than free energy, is the basic object in this approach that exploits a recently introduced microcanonical Monte Carlo method.     

Spin-glass transition in disordered terbium

While crystalline Tb is a helix antiferromagnet with a Néel temperature of 229 K which becomes ferromagnetic at 222 K, disordered Tb exhibits a spin-glass transition. The spin-glass freezing temperature ranges from 183 to 53 K, the lowest temperatures corresponding to the greatest degree of atomic disorder. These experiments constitute the first evidence for an elemental spin-glass.     

Superconductor-insulator transition in disordered boson-superlattices

We calculate the transport properties of a disordered Bose condensate. A superlattice made from two-dimensional planes of bosons in the condensate phase is considered. The disorder is due to charged impurities. We consider a homogeneous distribution of impurities and also impurities randomly distributed in planes. The dispersion relation of the collective excitations (plasmons) for the clean boson superlattice is calculated. The disorder induced phase transiton from a superfluid phase to an insulator phase is discussed and the static conductivity ( _c ) at the transition point is expressed in terms of the microscopic parameters of the model. For strongly coupled planes we find that _c is of ordere ²/h. The relation of our theoretical results to experiments with high-temperature superconductors is discussed.     

Continuous phase transition in a disordered eight-states Potts model

We investigate the two-dimensional eight-states ferromagnetic Potts model in the Voronoi-Delaunay tessellation. In this study, we assume that the coupling factor J varies with the distance r between the first neighbors as , with . The disordered system is simulated applying the single-cluster Monte-Carlo update algorithm and the reweighting technique. We find that this model displays a first-order phase transition if , in agreement with previous recent studies. For and 1.0, a typical second order transition is observed and the critical exponents for magnetization and susceptibility are calculated. Received 19 May 1999 and Received in final form 2 June 1999     

Commensurate-incommensurate transition in one-dimensional disordered systems

Commensurate-incommensurate transition in the one-dimensional disordered system is investigated and the soliton density near commensurability at high and low temperatures is obtained.     

Localization-delocalization transition in non-hermitian disordered systems

Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at short distances. We calculate the joint probability of complex eigenvalues and some other correlation functions. We find that the transition is abrupt and it is due to an interplay between two saddle points in the free energy functional.     

Multichannel scattering in a 1D disordered chain

The vector recursion method is generalized to a multichannel scattering formalism and used to study the transmittance in a one-dimensional model with an s-d hybridized Hamiltonian. The transmittance and wavefunctions of the s and d channels are studied.     

Multifloquet to single electronic channel transition in the transport properties of a resistive 1D driven disordered ring

We investigate the dc response of a 1D disordered ring coupled to a reservoir and driven by a magnetic flux with a linear dependence on time. We identify two regimes: (i) A localized or large length L regime, characterized by a dc conductance, g(dc), whose probability distribution P(g(dc)) is identical to the one exhibited by a 1D wire of the same length L and disorder strength placed in a two terminal Landauer setup and (ii) a multifloquet regime for small L and weak coupling to the reservoir, which exhibits large currents and conductances that can be g(dc)>1, in spite of the fact that the ring contains spinless electrons and a single electronic transmission channel. The crossover length between the multifloquet to the single-channel transport regime Lc is controlled by the coupling to the reservoir.     

Nonequilibrium wetting transition in a nonthermal 2D Ising model

Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E _c . Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model.     

Superconducting-insulator transition in disordered Josephson junctions networks

The superconducting-insulator transition is simulated in disordered networks of Josephson junctions with thermally activated Arrhenius-like resistive shunt. By solving the conductance matrix of the network, the transition is reproduced in different experimental conditions by tuning thickness, charge density and disorder degree. In particular, on increasing fluctuations of the parameters entering the Josephson coupling and the Coulomb energy of the junctions, the transition occurs for decreasing values of the critical temperature T _c and increasing values of the activation temperature T _o . The results of the simulation compare well with recent experiments where the mesoscopic fluctuations of the phase have been suggested as the mechanism underlying the phenomenon of emergent granularityin otherwise homogeneous films. The proposed approach is compared with the results obtained on TiN films and nanopatterned arrays of weak-links, where the superconductor-insulator transition is directly stimulated.     

Asymmetric metal-insulator transition in disordered ferromagnetic films

We present experimental data and a theoretical interpretation of the conductance near the metal-insulator transition in thin ferromagnetic Gd films of thickness b ≈ 2-10 nm. A large phase relaxation rate caused by scattering of quasiparticles off spin-wave excitations renders the dephasing length L(?) ? b in the range of sheet resistances considered, so that the effective dimension is d = 3. The conductivity data at different stages of disorder obey a fractional power-law temperature dependence and collapse onto two scaling curves for the metallic and insulating regimes, indicating an asymmetric metal-insulator transition with two distinctly different critical exponents; the best fit is obtained for a dynamical exponent z ≈ 2.5 and a correlation (localization) length critical exponent ν- ≈ 1.4 (ν+ ≈ 0.8) on the metallic (insulating) side.     

Delocalization transition of two-dimensional disordered systems in a strong magnetic field

The delocalization transition in two-dimensional systems and a strong magnetic field is investigated with respect to its dependence on the Landau band indexj and on the type of disorder. The generation of random potentials according to a given correlation functionf and for a chosen correlation lengthd is described. The spectral properties of random eigenvalue sequences are examined as measures for the extension of wavefunctions and indicate a nonuniversal delocalization behaviour in higher Landau bands for short ranged correlated potentials. The critical exponents of the localization length of wavefunctions are determined for rapidly varying potentials in the second lowest Landau band (j=1) and depend on the correlation lengthd of the disorder. This different critical behaviour compared to that in the lowest band is confirmed by calculations for the density-density correlations of wavefunctions at the centers of the Landau levels. Calculations in different geometries also show that the critical systems of delocalized states are conformal invariant in the case of the nonuniversal delocalization transition (dl ₀), whereas such local rescaling properties cannot be expected for slowly varying potentials.     

The topological structure of 2D disordered cellular systems

We analyze the structure of two dimensional disordered cellular systems generated by extensive computer simulations. These cellular structures are studied as topological trees rooted on a central cell or as closed shells arranged concentrically around a germ cell. We single out the most significant parameters that characterize statistically the organization of these patterns. Universality and specificity in disordered cellular structures are discussed. Received: 23 September 1997 / Received in final form: 14 January 1998 / Accepted: 29 January 1998     

Critical quantum chaos in 2D disordered systems with spin-orbit coupling

We examine the validity of the recently proposed semi-Poisson level spacing distribution function P(S), which characterizes “critical quantum chaos”, in 2D disordered systems with spin-orbit coupling. At the Anderson transition we show that the semi-Poisson P(S) can describe closely the critical distribution obtained with averaged boundary conditions, over Dirichlet in one direction with periodic in the other and Dirichlet in both directions. We also obtain a sub-Poisson linear number variance , with asymptotic value . The obtained critical statistics, intermediate between Wigner and Poisson, is discussed for disordered systems and chaotic models. Received 1 September 1999     

Phase transition in an occupationally disordered sulfate system

We have investigated the behavior of the Li_1.43Cs_0.57SO₄ single-crystal Raman spectra and dielectric permittivity as a function of temperature. It was observed that the crystal, which is an occupationally disordered system, with orthorhombic C_2v² structure at room temperature, undergoes a phase transition at 230 K. In the new phase the SO₄ tetrahedra remain in two non-equivalent sites and there is no evidence of the doubling of the unit cell.