A new metallic state in two dimensions

We report the discovery of a new and unexpected kind of metal in two dimensions (2D), which exists in the presence of scattering by local magnetic moments. The experiment was carried out on a 2D electron system in silicon, where the local magnetic moments have been induced by disorder and their number was varied using substrate bias (V_sub). In the new metal, the conductivity decreases as σ(n_s,T)=σ(n_s,T=0)+A(n_s)T² (n_s – carrier density) to a non-zero value as temperature T→0. In three dimensions, this T² dependence is well known, and results from Kondo scattering by local magnetic moments. In 2D, however, the existence of a metal with dσ/dT>0 is very surprising. As the number of local moments is reduced, the range of temperatures [T<T_m(V_sub)] where they dominate transport becomes smaller. For T>T_m, we observe the usual 2D metallic behavior with dσ/dT<0.     

Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions

We consider an interacting homogeneous Bose gas at zero temperature in two spatial dimensions. The properties of the system can be calculated as an expansion in powers of g, where g is the coupling constant. We calculate the ground state pressure and the ground state energy density to second order in the quantum loop expansion. The renormalization group is used to sum up leading and subleading logarithms from all orders in perturbation theory. In the dilute limit, the renormalization group improved pressure and energy density are expansions in powers of the T ^2B and T ^2Bln(T ^2B), respectively, where T ^2B is the two-body T-matrix. Received 19 April 2002 Published online 13 August 2002     

Phase transitions in two dimensions

Recent developments - both theoretical and experimental - in the understanding of phase transitions in two-dimensional systems are reviewed. Topics discussed include the classification and characterization of order/disorder transitions in adsorbed monolayers, the breakdown of universality, superfluidity in helium films and the critical behaviour of the two-dimensional XY model, Abelian and non-Abelian symmetry and the analogies between the theory of phase transitions in two dimensions and quantum field theory, especially quark confinement, in four-dimensional space time.     

Critical temperature of interacting Bose gases in two and three dimensions

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.     

Glassy features of a Bose glass

We study a two-dimensional Bose-Hubbad model at a zero temperature with random local potentials in the presence of either uniform or binary disorder. Many low-energy metastable configurations are found with virtually the same energy as the ground state. These are characterized by the same blotchy pattern of the, in principle, complex nonzero local-order parameter as the ground state. Yet, unlike the ground state, each island exhibits an overall random independent phase. The different phases in different coherent islands could provide a further explanation for the lack of coherence observed in experiments on Bose glasses.     

On the random antiphase state in the ± J spin glass model in two dimensions

Numerical calculations of a ground state and the rigidity have been made for samples of 50 × 50 Ising spins interacting via ± J bonds on a square lattice using Edmond's algorithm, a method well established in optimization theory. For some value of the concentration (0.1<x<0.2) of antiferromagnetic bonds (-J), an ordered (rigid) state occurs with zero magnetization due to magnetic wall separating domains of opposite spins. This new phase, here named a random antiphase state, could be an intermediate phase between ferromagnetism and paramagnetism.     

Local-field correction of the charged Bose condensate for two and three dimensions

The local-field correction for the dielectric function of the two-dimensional and of the three-dimensional Bose condensate is calculated within a sum-rule version of the Singwi et al. (Phys. Rev.176, 589 (1968)) approach. We derive analytical expressions for small and large wave numbers and give analytical expressions for the density dependence. We compare the results of the groundstate energy for the three-dimensional system with Monte-Carlo computations. In two dimensions a roton structure in the plasmon dispersion is found at low boson density. The plasmon density of states is calculated. A correlation induced charge-density-wave instability in layered structures of two-dimensional Bose gases is discussed.     

Bounds for a Bose condensate in dimensions v ⩾ 3

A stronger version of the Bogoliubov inequality is used to derive an upper bound for the anomalous average ¦x)>|s of an interacting nonrelativislic Bose fielda(x) at a finite temperature. This bound is ¦a(x)²|s <pR, whereR satisfies 1 -R = (RT/2T _c ^v/2, withv the dimensionality, andT _c the critical temperature in the absence of interactions. The formation of nonzero averages is closely related to the Bose-Einstein condensation and ¦|·² is often believed to coincide with the mean densitypa of the condensate. We have found nonrigorous arguments supporting the inequality po ? ¦|·², which parallels the result of Griffiths in the case of spin systems.     

Relaxation to spin glass ground state in one to six dimensions

In the ±J Edwards-Anderson spin glass, we find by Monte Carlo simulation the (approximate) ground state energy. Also we check how in the relaxation towards this ground state the fraction of never flipped spins diminishes with time.     

In one and two dimensions,every stationary measure for a stochastic Ising Model is a Gibbs state

It is shown that one and two dimensional (generalized) stochastic Ising models with finite range potentials have only Gibbs states as their stationary measures. This is true even if the stationary measure or the potential is not translation invariant. This extends previously known results which are restricted to translation invariant stationary measures and potentials. In particular if the potential has only one Gibbs state the stochastic Ising Model must be ergodic.Research supported in part by N.S.F. Grant MPS 74-18926Alfred P. Sloan Fellow     

Spin-polarized ground state for interacting electrons in two dimensions

We study numerically the ground state magnetization for clusters of interacting electrons in two dimensions in the regime where the single particle wave functions are localized by disorder. It is found that the Coulomb interaction leads to a spontaneous ground state magnetization. For a constant electronic density, the total spin increases linearly with the number of particles, suggesting a ferromagnetic ground state in the thermodynamic limit. The magnetization is suppressed when the single particle states become delocalized.     

The disordered Bose condensate in two dimensions: application to high-Tc superconductors

We calculate the dynamical conductivity for a weakly disordered Bose condensate in two dimensions. The disorders is due to neutral impurities. We compare the asymptotic laws (for small and large frequencies) for neutral impurities with the ones for charged impurities. Universal functions for the dynamical transport properties are derived. The plasmon density of states shows a linear increase with energy for intermediate energies and a peak structure at larger energies. Our theoretical results are compared with experimental results (far-infrared, electron-energy-loss and Raman spectroscopy) found in the high-T_c superconductor YBa₂Cu₃O_7−δ. The occurrence of a quasi-gap in a disordered Bose condensate is described and discussed in connection with experiments on high-T_c superconductors.     

A new discrete Edwards model and a new polymer measure in two dimensions

The new discrete Edwards models in this paper are defined in terms of the so-called restricted intersection local times of the lattice random walk in two dimensions. We study the asymptotic behaviours of these new discrete Edwards models in the superrenormalizable cases. In particular, by approximating these models we can construct new polymer measures in two dimensions which are different from the original polymer measures obtained by approximating the original discrete Edwards models. The new discrete Edwards models can be thought of as zero-component lattice ω⁴-fields with different cutoffs in the free and interacting parts.     

Phase transition to the conducting state in a system of charge-transfer excitons at a donor-acceptor interface

We discuss the phase transition to the conducting state in a system of 2D charge-transfer excitons (CTEs) at a donor-acceptor interface. The phase transition arises due to strong dipole-dipole repulsion between CTEs which stimulates the population of free carriers in higher energy states even at low temperature. We use the computer simulations with the random distribution of excitons, with finite lifetime explicitly taken into account. The critical concentration of CTEs and their energy distribution are calculated. We also discuss the possibility of observing the predicted phenomena. Fiz. Tverd. Tela (St. Petersburg) 41, 781–784 (May 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Absence of symmetry breaking forN-vector spin glass models in two dimensions

We prove the absence of continuous symmetry breaking at arbitrary temperatures for two-dimensionalN-vector spin glass models with Hamilton function $$H = - \sum\limits_{i,j} {J(i,j)\left| {i - j} \right|^{ - 2 - \varepsilon } S_i \cdot S_j ,} \varepsilon > 0$$ whereJ (i, j) has mean 0 and variance 1, for alli, j. We comment on the role of boundary conditions in spin glasses and on their critical behaviour in high dimensions.     

Phase fluctuations in atomic Bose gases

We improve on the Popov theory for partially Bose-Einstein condensed atomic gases by treating the phase fluctuations exactly. As a result, the theory becomes valid in arbitrary dimensions and is able to describe the low-temperature crossover between three-, two-, and one-dimensional Bose gases, which is currently being explored experimentally. We consider both homogeneous and trapped Bose gases.     

Phase separation on regular and fractal lattices in two dimensions

A stochastic reorganization model is simulated on a two-dimensional square lattice, where we investigate finite size effects, and on clusters generated by diffusion limited aggregation. We propose a simple mean-field model, which accounts well for the data.