Non-perturbative corrections to mean-field behavior: spherical model on spider-web graph

We consider the spherical model on a spider-web graph. This graph is effectively infinite-dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We first determine all normal modes of the coupled springs problem on this graph, using its large symmetry group. In the thermodynamic limit, the spectrum is a set of $\delta$-functions, and all the modes are localized. The fractional number of modes with frequency less than $\omega$ varies as $\exp (-C/\omega)$ for $\omega$ tending to zero, where $C$ is a constant. For an unbiased random walk on the vertices of this graph, this implies that the probability of return to the origin at time $t$ varies as $\exp(- C' t^{1/3})$, for large $t$, where $C'$ is a constant. For the spherical model, we show that while the critical exponents take the values expected from the mean-field theory, the free-energy per site at temperature $T$, near and above the critical temperature $T_c$, also has an essential singularity of the type $\exp[ -K {(T - T_c)}^{-1/2}]$.Comment: substantially revised, a section adde

Real-space entanglement spectra of parton states in fractional quantum Hall systems

Real-space entanglement spectra (RSES) capture characteristic features of the topological order encoded in the fractional quantum Hall (FQH) states. In this work, we numerically compute, using Monte Carlo methods, the RSES and the counting of edge excitations of non-Abelian FQH states constructed using the parton theory. Efficient numerical computation of RSES of parton states is possible, thanks to their product-of-Slater-determinant structure, allowing us to compute the spectra in systems of up to 80 particles. Specifically, we compute the RSES of the parton states $\phi_2^2$, $\phi_2^3$, and $\phi_3^2$, where $\phi_n$ is the wave function of $n$ filled Landau levels, in the ground state as well as in the presence of bulk quasihole states. We then explicitly demonstrate a one-to-one correspondence of RSES of the parton states with representations of the Kac-Moody algebras satisfied by their edge currents. We also show that for the lowest Landau level projected version of these parton states, the spectra match with that obtained from the edge current algebra. We also perform a computation of spectra of the overlap matrices corresponding to the edge excitations of the parton states with a constrained number of particles in the different parton Landau levels. Counting in these matches the individual branches present in RSES, providing insight about how different branches are formed

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Direct imaging of nanoscale field-driven domain wall oscillations in Landau structures

Linear oscillatory motion of domain walls (DWs) in the kHz and MHz regime is crucial when realizing precise magnetic field sensors such as giant magnetoimpedance devices. Numerous magnetically active defects lead to pinning of the DWs during their motion, affecting the overall behavior. Thus, the direct monitoring of the domain wall's oscillatory behavior is an important step to comprehend the underlying micromagnetic processes and to improve the magnetoresistive performance of these devices. Here, we report an imaging approach to investigate such DW dynamics with nanoscale spatial resolution employing conventional table-top microscopy techniques. Time-averaged magnetic force microscopy and Kerr imaging methods are applied to quantify the DW oscillations in Ni81Fe19 rectangular structures with Landau domain configuration and are complemented by numeric micromagnetic simulations. We study the oscillation amplitude as a function of external magnetic field strength, frequency, magnetic structure size, thickness and anisotropy and understand the excited DW behavior as a forced damped harmonic oscillator with restoring force being influenced by the geometry, thickness, and anisotropy of the Ni81Fe19 structure. This approach offers new possibilities for the analysis of DW motion at elevated frequencies and at a spatial resolution of well below 100 nm in various branches of nanomagnetism

Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes

We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical percolation threshold as a function of the ratio of sizes of discs, for different values of the relative areal densities of two discs, can be described in terms of a scaling function of only one variable. The recent accurate Monte Carlo estimates of critical threshold by Quintanilla and Ziff [Phys. Rev. E, 76 051115 (2007)] are in very good agreement with the proposed scaling relation.Comment: 4 pages, 3 figure

Coherent coupling between radio frequency, optical, and acoustic waves in piezo-optomechanical circuits

The interaction of optical and mechanical modes in nanoscale optomechanical systems has been widely studied for applications ranging from sensing to quantum information science. Here, we develop a platform for cavity optomechanical circuits in which localized and interacting 1550 nm photons and 2.4 GHz phonons are combined with photonic and phononic waveguides. Working in GaAs facilitates manipulation of the localized mechanical mode either with a radio frequency field through the piezo-electric effect, or optically through the strong photoelastic effect. We use this to demonstrate a novel acoustic wave interference effect, analogous to coherent population trapping in atomic systems, in which the coherent mechanical motion induced by the electrical drive can be completely cancelled out by the optically-driven motion. The ability to manipulate cavity optomechanical systems with equal facility through either photonic or phononic channels enables new device and system architectures for signal transduction between the optical, electrical, and mechanical domains

Self-assembly as a tool to study microscale curvature and strain-dependent magnetic properties

The extension of 2D ferromagnetic structures into 3D curved geometry enables to tune its magnetic properties such as uniaxial magnetic anisotropy. Tuning the anisotropy with strain and curvature has become a promising ingredient in modern electronics, such as flexible and stretchable magnetoelectronic devices, impedance-based field sensors, and strain gauges, however, has been limited to extended thin films and to only moderate bending. By applying a self-assembly rolling technique using a polymeric platform, we provide a template that allows homogeneous and controlled bending of a functional layer adhered to it, irrespective of its shape and size. This is an intriguing possibility to tailor the sign and magnitude of the surface strain of integrated, micron-sized devices. In this article, the impact of strain and curvature on the magnetic ground state and anisotropy is quantified for thin-film Permalloy micro-scale structures, fabricated on the surface of the tubular architectures, using solely electrical measurements

Electronically integrated microcatheters based on self-assembling polymer films

Existing electronically integrated catheters rely on the manual assembly of separate components to integrate sensing and actuation capabilities. This strongly impedes their miniaturization and further integration. Here, we report an electronically integrated self-assembled microcatheter. Electronic components for sensing and actuation are embedded into the catheter wall through the self-assembly of photolithographically processed polymer thin films. With a diameter of only about 0.1 mm, the catheter integrates actuated digits for manipulation and a magnetic sensor for navigation and is capable of targeted delivery of liquids. Fundamental functionalities are demonstrated and evaluated with artificial model environments and ex vivo tissue. Using the integrated magnetic sensor, we develop a strategy for the magnetic tracking of medical tools that facilitates basic navigation with a high resolution below 0.1 mm. These highly flexible and microsized integrated catheters might expand the boundary of minimally invasive surgery and lead to new biomedical applications. Copyright © 2021 The Authors, some rights reserved