Action at a distance in classical uniaxial ferromagnetic arrays

We examine in detail the theoretical foundations of striking long-range couplings emerging in arrays of fluid cells connected by narrow channels by using a lattice gas (Ising model) description of a system. We present a reexamination of the well known exact determination of the two-point correlation function along the edge of a channel using the transfer matrix technique and a new interpretation is provided. The explicit form of the correlation length is found to grow exponentially with the cross section of the channels at the bulk two-phase coexistence. The aforementioned result is recaptured by a refined version of the Fisher-Privman theory of first order phase transitions in which the Boltzmann factor for a domain wall is decorated with a contribution stemming from the point tension originated at its endpoints. The Boltzmann factor for a domain wall together with the point tension is then identified exactly thanks to two independent analytical techniques, providing a critical test of the Fisher-Privman theory. We then illustrate how to build up the network model from its elementary constituents, the cells and the channels. Moreover, we are able to extract the strength of the coupling between cells and express them in terms of the length and width and coarse grained quantities such as surface and point tensions. We then support our theoretical investigation with a series of corroborating results based on Monte Carlo simulations. We illustrate how the long range ordering occurs and how the latter is signaled by the thermodynamic quantities corresponding to both planar and three-dimensional Ising arrays.Comment: 36 pages, 19 figure

Non-equilibrium Dynamics of Finite Interfaces

We present an exact solution to an interface model representing the dynamics of a domain wall in a two-phase Ising system. The model is microscopically motivated, yet we find that in the scaling regime our results are consistent with those obtained previously from a phenomenological, coarse-grained Langevin approach.Comment: 12 pages LATEX (figures available on request), Oxford preprint OUTP-94-07

A necklace of Wulff shapes

In a probabilistic model of a film over a disordered substrate, Monte-Carlo simulations show that the film hangs from peaks of the substrate. The film profile is well approximated by a necklace of Wulff shapes. Such a necklace can be obtained as the infimum of a collection of Wulff shapes resting on the substrate. When the random substrate is given by iid heights with exponential distribution, we prove estimates on the probability density of the resulting peaks, at small density

The Role of the Dielectric Barrier in Narrow Biological Channels: a Novel Composite Approach to Modeling Single-channel Currents

A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approximately accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel is also calculated using the MD trajectory. Therefore, except for a reasonable choice of dielectric constants, no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielectric self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory

Collective Effects in Linear Spectroscopy of Dipole-Coupled Molecular Arrays

We present a consistent analysis of linear spectroscopy for arrays of nearest neighbor dipole-coupled two-level molecules that reveals distinct signatures of weak and strong coupling regimes separated for infinite size arrays by a quantum critical point. In the weak coupling regime, the ground state of the molecular array is disordered, but in the strong coupling regime it has (anti)ferroelectric ordering. We show that multiple molecular excitations (odd/even in weak/strong coupling regime) can be accessed directly from the ground state. We analyze the scaling of absorption and emission with system size and find that the oscillator strengths show enhanced superradiant behavior in both ordered and disordered phases. As the coupling increases, the single excitation oscillator strength rapidly exceeds the well known Heitler-London value. In the strong coupling regime we show the existence of a unique spectral transition with excitation energy that can be tuned by varying the system size and that asymptotically approaches zero for large systems. The oscillator strength for this transition scales quadratically with system size, showing an anomalous one-photon superradiance. For systems of infinite size, we find a novel, singular spectroscopic signature of the quantum phase transition between disordered and ordered ground states. We outline how arrays of ultra cold dipolar molecules trapped in an optical lattice can be used to access the strong coupling regime and observe the anomalous superradiant effects associated with this regime.Comment: 12 pages, 7 figures main tex

Thickness dependent magnetotransport in ultra-thin manganite films

To understand the near-interface magnetism in manganites, uniform, ultra-thin films of La_{0.67}Sr_{0.33}MnO_3 were grown epitaxially on single crystal (001) LaAlO_3 and (110) NdGaO_3 substrates. The temperature and magnetic field dependent film resistance is used to probe the film's structural and magnetic properties. A surface and/or interface related dead-layer is inferred from the thickness dependent resistance and magnetoresistance. The total thickness of the dead layer is estimated to be $\sim 30 \AA$ for films on NdGaO_3 and $\sim 50 \AA$ for films on LaAlO_3.Comment: 11 pages, 4 figure