Two-dimensional metal-insulator transition as a percolation transition in a high-mobility electron system

By carefully analyzing the low temperature density dependence of 2D conductivity in undoped high-mobility n-GaAs heterostructures, we conclude that the 2D metal-insulator transition in this 2D electron system is a density inhomogeneity driven percolation transition due to the breakdown of screening in the random charged impurity disorder background. In particular, our measured conductivity exponent of approximately 1.4 approaches the 2D percolation exponent value of 4/3 at low temperatures and our experimental data are inconsistent with there being a zero-temperature quantum critical point in our system.     

3d Monte Carlo simulation of site-bond continuum percolation of spheres

We present off-lattice Monte Carlo simulations of site-bond percolation of semi-penetrable spheres or, equivalently, of hard spheres with a finite bond range. We will show that the crucial parameter is the effective volume fraction ( φ_e), i.e. the volume that is occupied or within the bond range of at least one particle. For the equivalent system of semi-penetrable spheres 1 - φ_e is the porosity. The bond percolation threshold (p _b) can be described in terms of φ_e by a simple analytical expression: log(φ_e)/log(φ_ec) + log(p _b)/log(p _bc) = 1, with p _bc = 0.12 independent of the bond range and φ_ec a constant that decreases with increasing bond range. Received: 10 March 2003 / Accepted: 23 April 2003 / Published online: 21 May 2003 RID="a" ID="a"e-mail: jean-christophe.gimel@univ-lemans.fr     

Simulation of the united site-bond problem with separation of bonds in percolation theory

The 2D percolation mixed problem is solved in a computer experiment on a square lattice with separation of the probabilities of formation of horizontal and vertical bonds. The extrema and form of dependences are determined.     

Monte Carlo study of phase diagram for correlated site-bond percolation in two dimensions

At the critical point of the square Ising model, the percolation threshold for randomly active bonds between up spins is close top _Bc =0.60 and seems compatible with the predictionp _Bc =1-exp(–2J/k _B T _c )=0.586 of Coniglio and Klein. Longer simulations on larger lattices are necessary for a more precise clarification.     

Flutter of a buckled plate as an example of chaotic motion of a deterministic autonomous system

For aeroelasticity of plates and shells, the equations of motion are well established. Results obtained by numerical time integration have been compared to those obtained by topological theories of dynamics and also from experiment. All of these suggest that chaotic self-excited oscillations may occur for this deterministic system.     

Random percolation as a gauge theory

Three-dimensional bond or site percolation theory on a lattice can be interpreted as a gauge theory in which the Wilson loops are viewed as counters of topological linking with random clusters. Beyond the percolation threshold large Wilson loops decay with an area law and show the universal shape effects due to flux tube quantum fluctuations like in ordinary confining gauge theories. Wilson loop correlators define a non-trivial spectrum of physical states of increasing mass and spin, like the glueballs of ordinary gauge theory. The crumbling of the percolating cluster when the length of one periodic direction decreases below a critical threshold accounts for the finite temperature deconfinement, which belongs to 2D percolation universality class.     

Fe nanowires in carbon nanotubes as an example of a one-dimensional system of exchange-coupled ferromagnetic nanoparticles

The cooperative phenomena revealed in the field and temperature dependences of the magnetization in a system of iron nanoparticles in carbon nanotubes were studied experimentally. The character of the temperature dependences of the magnetization indicates that the ferromagnetic Fe particles in carbon nanotubes are exchange-coupled. In the region where the magnetization approaches saturation, the magnetization curves reveal the power dependence ΔM～ H^?3/2 typical for a one-dimensional system of exchange-coupled ferromagnetic nanoparticles.     

Fluorine dynamics in BaF2 crystal lattice as an example of complex motion in a simple system

Fluorine relaxation profiles for a BaF₂ single crystal collected at several temperatures have been analyzed in terms of essentially different motional models: free rotational and free translational diffusion. The analysis has been performed to critically review the sensitivity of field dependent relaxation studies to mechanisms of molecular motions. The tested motional models do not realistically describe the fluorine dynamics within the crystal lattice. They have been chosen to attempt to answer quite fundamental questions regarding the feasibility of the field dependent nuclear spin relaxation studies to provide unique information on dynamic processes: 1. Is it possible to get information about the motional mechanisms by analyzing relaxation profiles collected in a broad frequency range? 2. To what extent is it possible to reasonably reproduce relaxation profiles in terms of unrealistic motional models?It has been concluded from the analysis that the rotational model leading to a single exponential correlation function explains the experimental data much better than the translational one. Validity regimes of the second order perturbation theory have been discussed in the context of the investigated system and the applied models.     

Thermodynamic properties of the site-bond diluted Ising ferromagnet on an anisotropic square lattice

Within the framework of an effective-field theory, we calculate the magnetization, specific heat and susceptibility of a quenched site-bond diluted Ising ferromagnet on a square lattice with both anisotropic coupling constants and anisotropic bond occupancy probabilities. It is shown that these thermodynamic quantities exhibit some interesting behavior as a function of temperature for selected concentrations of magnetic atoms and anisotropic bonds with anisotropic coupling constants.     

An example of a phase transition in an open pseudobimolecular system

A phase transition at microscopic level is exhibited for an open bimolecular chemical system. We also give another interpretation of an apparent incompatibility between the microscopic and the macroscopic analysis shown by J. Keizer.     

Charge transfer between percolation levels in a system with an artificial,strongly disordered potential

We observe a hysteresis in the magnetoresistance of mesoscopic samples with a disordered antidot lattice. When the Fermi level lies in between two Landau levels, the Faraday electric field induces a change in the charge of two closed, intercalated electron trajectories in the artificial strongly disordered potential. The total transferred charge is approximately equal to 40e. Depending on whether this transfer is towards the inner or outer closed trajectory (which is determined by the direction of the magnetic field sweep) the potential barrier for trajectories that traverse the sample will increase or decrease.     

Hirota equation as an example of an integrable symplectic map

The Hamiltonian formalism is developed for the sine-Gordon model on the spacetime light-like lattice, first introduced by Hirota. The evolution operator is explicitly constructed in the quantum variant of the model and the integrability of the corresponding classical finite-dimensional system is established.     

Phase transitions in superionics as an example of a modified Pott's model

We proposed a theory of superionic conductors based on the properties of theq-state Pott's model. The strong first order transition of this model for largeq gives an explanation for the sudden release of the cations at the superionic transition. Using modified versions of the model, in which we destroy its symmetry, we find that depending on the parameters, we can have no transition, one first order transition or a first order transition followed (if the temperature increases) by a second order transition.     

Two-dimensional exciton-phonon system in a magnetic field

The properties of an exciton at the surface of a polar crystal in a weak magnetic fieldB, which is perpendicular to the surface and is constant, are discussed by a perturbational method. Taking account of the effects from the surface modes of the lattice vibrations and on ground of a slow motion of the exciton, the self-energy of an exciton, the effective potential and renormalized masses are derived. The self-energy of the exciton becomes higher under the action of the magnetic field.Center of Theoretical Physics, CCAST (World Laboratory)     

Transport and percolation in a low-density high-mobility two-dimensional hole system

We present a study of the temperature and density dependence of the resistivity of an extremely high quality two-dimensional hole system grown on the (100) surface of GaAs. For high densities in the metallic regime (p > or approximately4x10;{9} cm;{-2}), the nonmonotonic temperature dependence ( approximately 50-300 mK) of the resistivity is consistent with temperature dependent screening of residual impurities. At a fixed temperature of T=50 mK, the conductivity versus density data indicate an inhomogeneity driven percolation-type transition to an insulating state at a critical density of 3.8x10;{9} cm;{-2}.     

Antiferromagnetic material with the magnetoelectric effect as an example of a left-handed medium

The propagation of electromagnetic waves in an antiferromagnetic material with the magnetoelectric effect is theoretically studied. The frequency dependences of the wavenumbers, dynamical permeability and permittivity, and reflection coefficient of electromagnetic waves for various energy parameters of the antiferromagnetic material have been obtained. It has been shown that there is a frequency range where the dynamical permeability and permittivity, as well as one of the wavenumbers, are simultaneously negative in the antiferromagnetic material with the magnetoelectric effect. In this case, the antiferromagnetic material is an example of a so-called left-handed medium. The reflection coefficient of electromagnetic waves from the surface of the antiferromagnetic material decreases anomalously in this frequency range.     

Investigation of the percolation transition in a nonwetting liquid-nanoporous medium system

The flows of liquid into and out of a nanoporous medium are studied as processes leading to the fluctuation formation and the growth of fractal clusters of filled and empty pores, respectively. The conditions for stable growth of such fluctuations are analyzed as a function of the interfacial energy between the liquid and the porous medium and the surface energy of the liquid. Expressions are obtained for the pressure at which the barrier for fluctuation filling and emptying of the pores vanishes. In general, it is shown for porous media with a pore-size distribution that these processes can be interpreted as a percolation phase transition. The volume and susceptibility of a liquid-porous medium system near the transition points with inflow and outflow of the liquid are calculated. The phenomenon of nonoutflow of a nonwetting liquid from a porous medium and hysteresis of the flow of liquid into and out of a porous medium are explained on the basis of the mechanism considered. The results of an experimental investigation of these processes in the system liquid Wood’s alloy-silochrome 80 and silochrome 120 are presented. The experimental data obtained can be described on the basis of the proposed mechanism.