The method of the preceding paper is used to derive approximate results for the spin-spin correlation functions of a ferromagnet with dipole-dipole coupling between spins. This formalism employs the drone-fermion representation for spin f and a high density l/z classification of terms. Results are obtained for the spin wave energy and damping as functions of momentum and temperature. As in the case of the Heisenberg model, it is found that the damping is small for any temperature below T, for sufficiently long wavelengths.
In this paper, we propose a surface-adaptable all-metal micro-four-point probe (μ4PP) with a unique configuration. The μ4PP consists of four independent metallic sub-cantilevers with sharp Cu tips, and an SU-8 body structure to support the sub-cantilevers. The tip height is approximately 15 μm, and the tips are fabricated by anisotropic wet-etching of silicon followed by Cu electroplating. Each metallic cantilever connected to the SU-8 body structure acts as a flexible spring, so that the conducting tip can make gentle, non-destructive contact with fragile surfaces. To enhance the adhesion between the metallic sub-cantilevers and the SU-8 body, mushroom-shaped Cu structures were fabricated using an under-baked and under-exposed photolithography process. Various μ4PPs were designed and fabricated to verify their diverse range of applications, and preliminary experiments were performed using these fabricated μ4PPs. The resultant flexibility and reliability were experimentally confirmed on several samples, such as a polymer cantilever, a graphene flake, and curved metallic surfaces. We also expect that the proposed μ4PP will be suitable for measuring the anisotropic characteristics of crystal materials or the Hall effect in semiconductors.
We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdős-Rényi (E-R) random graph is determined by the average degree k and p(s) undergoes a dramatic change when k is varied around the critical point of the percolation transition, k = 1. When k 1, the p(s) is described by the statistics of the Gaussian orthogonal ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at k = 1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brodydistribution. Furthermore, below the critical point p(s) can be given with the help of the regularized Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the internet, a word association network and a protein-protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E-R graph.
We have measured the optical reflectivity (0.5-4 eV) of metallic Si in the primitive hexagonal (PHI phase at pressures of 16 to 35 GPa. The dominant optical absorption near 2.5 eV is explained in terms of interband excitations
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