Mapping vesicle shapes into the phase diagram: A comparison of experiment and theory

Phase-contrast microscopy is used to monitor the shapes of micron-scale fluid-phase phospholipid-bilayer vesicles in aqueous solution. At fixed temperature, each vesicle undergoes thermal shape fluctuations. We are able experimentally to characterize the thermal shape ensemble by digitizing the vesicle outline in real time and storing the time-sequence of images. Analysis of this ensemble using the area-difference-elasticity (ADE) model of vesicle shapes allows us to associate (map) each time-sequence to a point in the zero-temperature (shape) phase diagram. Changing the laboratory temperature modifies the control parameters (area, volume, etc.) of each vesicle, so it sweeps out a trajectory across the theoretical phase diagram. It is a nontrivial test of the ADE model to check that these trajectories remain confined to regions of the phase diagram where the corresponding shapes are locally stable. In particular, we study the thermal trajectories of three prolate vesicles which, upon heating, experienced a mechanical instability leading to budding. We verify that the position of the observed instability and the geometry of the budded shape are in reasonable accord with the theoretical predictions. The inability of previous experiments to detect the ``hidden'' control parameters (relaxed area difference and spontaneous curvature) make this the first direct quantitative confrontation between vesicle-shape theory and experiment.Comment: submitted to PRE, LaTeX, 26 pages, 11 ps-fi

Towards analytic description of a transition from weak to strong coupling regime in correlated electron systems. I. Systematic diagrammatic theory with two-particle Green functions

We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals metal-insulator transition at half filling and gives rise to a new vanishing ``Kondo'' scale causing breakdown of weak-coupling perturbation theory. To describe the critical behavior at the metal-insulator transition a novel, self-consistent diagrammatic technique with two-particle Green functions is developed. The theory is based on the linked-cluster expansion for the thermodynamic potential with electron-electron interaction as propagator. Parquet diagrams with a generating functional are derived. Numerical instabilities due to the metal-insulator transition are demonstrated on simplifications of the parquet algebra with ring and ladder series only. A stable numerical solution in the critical region is reached by factorization of singular terms via a low-frequency expansion in the vertex function. We stress the necessity for dynamical vertex renormalizations, missing in the simple approximations, in order to describe the critical, strong-coupling behavior correctly. We propose a simplification of the full parquet approximation by keeping only most divergent terms in the asymptotic strong-coupling region. A qualitatively new, feasible approximation suitable for the description of a transition from weak to strong coupling is obtained.Comment: 17 pages, 4 figures, REVTe

The free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a variety of other spin systems generally assumed to belong to the same critical universality class. In particular, we have also derived the analogous expansions for the Ising models with spin s=1,3/2,.. and for the lattice euclidean scalar field theory with quartic self-interaction, on the simple cubic and the body-centered cubic lattices. Our bivariate high-temperature expansions, which extend through K^24, enable us to compute, through the same order, all higher derivatives of the free energy with respect to the field, namely all higher susceptibilities. These data make more accurate checks possible, in critical conditions, both of the scaling and the universality properties with respect to the lattice and the interaction structure and also help to improve an approximate parametric representation of the critical equation of state for the three-dimensional Ising model universality class.Comment: 22 pages, 10 figure

Cumulant expansion of the periodic Anderson model in infinite dimension

The diagrammatic cumulant expansion for the periodic Anderson model with infinite Coulomb repulsion ($U=\infty$) is considered here for an hypercubic lattice of infinite dimension ($d=\infty$). The same type of simplifications obtained by Metzner for the cumulant expansion of the Hubbard model in the limit of $d=\infty$, are shown to be also valid for the periodic Anderson model.Comment: 13 pages, 7 figures.ps. To be published in J. Phys. A: Mathematical and General (1997

Theory of NMR as a local probe for the electronic structure in the mixed state of the high-TcT_c cuprates

We argue that nuclear magnetic resonance experiments are a site-sensitive probe for the electronic spectrum in the mixed state of the high-$T_c$ cuprates. Within a spin-fermion model, we show that the Doppler-shifted electronic spectrum arising from the circulating supercurrent changes the low-frequency behavior of the imaginary part of the spin-susceptibility. For a hexagonal vortex lattice, we predict that these changes lead to {\it (a)} a unique dependence of the $^{63}$Cu spin lattice relaxation rate, $1/T_1$, on resonance frequency, and {\it (b)} a temperature dependence of $T_1$ which varies with frequency. We propose a nuclear quadrupole experiment to study the effects of a uniform supercurrent on the electronic structure and predict that $T_1$ varies with the direction of the supercurrent.Comment: RevTex, 5 pages, 3 figures embedded in the tex

Solitary Waves of Planar Ferromagnets and the Breakdown of the Spin-Polarized Quantum Hall Effect

A branch of uniformly-propagating solitary waves of planar ferromagnets is identified. The energy dispersion and structures of the solitary waves are determined for an isotropic ferromagnet as functions of a conserved momentum. With increasing momentum, their structure undergoes a transition from a form ressembling a droplet of spin-waves to a Skyrmion/anti-Skyrmion pair. An instability to the formation of these solitary waves is shown to provide a mechanism for the electric field-induced breakdown of the spin-polarized quantum Hall effect.Comment: 5 pages, 3 eps-figures, revtex with epsf.tex and multicol.st

Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices

High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these quantities enter into a sequence of universal amplitude-ratios which determine the critical equation of state. We have obtained a substantial extension through order 24, of the high-temperature expansions of the free energy (in presence of a magnetic field) for the Ising models with spin s >= 1/2 and for the lattice scalar field theory with quartic self-interaction, on the simple-cubic and the body-centered-cubic lattices in four, five and six spatial dimensions. A numerical analysis of the higher susceptibilities obtained from these expansions, yields results consistent with the widely accepted ideas, based on the renormalization group and the constructive approach to Euclidean quantum field theory, concerning the no-interaction ("triviality") property of the continuum (scaling) limit of spin-s Ising and lattice scalar-field models at and above the upper critical dimensionality.Comment: 17 pages, 10 figure

Linked Cluster Expansion Around Mean-Field Theories of Interacting Electrons

A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field theories at weak (Hartree-Fock) and strong (Hubbard-III) coupling the expansion represents a universal and comprehensive tool for systematic improvements of static mean-field theories. As an example of the general formalism we investigate in detail an analytically tractable series of ring diagrams that correctly capture dynamical fluctuations at weak coupling. We introduce renormalizations of the diagrammatic expansion at various levels and show how the resultant theories are related to other approximations of similar origin. We demonstrate that only fully self-consistent approximations produce global and thermodynamically consistent extensions of static mean field theories. A fully self-consistent theory for the ring diagrams is reached by summing the so-called noncrossing diagrams.Comment: 17 pages, REVTEX, 13 uuencoded postscript figures in 2 separate file

Vicinal Surfaces and the Calogero-Sutherland Model

A miscut (vicinal) crystal surface can be regarded as an array of meandering but non-crossing steps. Interactions between the steps are shown to induce a faceting transition of the surface between a homogeneous Luttinger liquid state and a low-temperature regime consisting of local step clusters in coexistence with ideal facets. This morphological transition is governed by a hitherto neglected critical line of the well-known Calogero-Sutherland model. Its exact solution yields expressions for measurable quantities that compare favorably with recent experiments on Si surfaces.Comment: 4 pages, revtex, 2 figures (.eps

Nonlocal Conductivity in the Vortex-Liquid Regime of a Two-Dimensional Superconductor

We have simulated the time-dependent Ginzburg-Landau equation with thermal fluctuations, to study the nonlocal dc conductivity of a superconducting film. Having examined points in the phase diagram at a wide range of temperatures and fields below the mean-field upper critical field, we find a portion of the vortex-liquid regime in which the nonlocal ohmic conductivity in real space is negative over a distance several times the spacing between vortices. The effect is suppressed when driven beyond linear response. Earlier work had predicted the existence of such a regime, due to the high viscosity of a strongly-correlated vortex liquid. This behavior is clearly distinguishable from the monotonic spatial fall-off of the conductivity in the higher temperature or field regimes approaching the normal state. The possibilities for experimental study of the nonlocal transport properties are discussed.Comment: 18 pages, revtex, 6 postscript figure