Percolation on hyperbolic lattices

The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and reaches from the middle to the boundary. This transition is of the same type and has the same finite-size scaling properties as the corresponding transition for the Cayley tree. At the upper threshold, on the other hand, a single unbounded cluster forms which overwhelms all the others and occupies a finite fraction of the volume as well as of the boundary connections. The finite-size scaling properties for this upper threshold are different from those of the Cayley tree and two of the critical exponents are obtained. The results suggest that the percolation transition for the hyperbolic lattices forms a universality class of its own.Comment: 17 pages, 18 figures, to appear in Phys. Rev.

Anomalous response in the vicinity of spontaneous symmetry breaking

We propose a mechanism to induce negative AC permittivity in the vicinity of a ferroelectric phase transition involved with spontaneous symmetry breaking. This mechanism makes use of responses at low frequency, yielding a high gain and a large phase delay, when the system jumps over the free-energy barrier with the aid of external fields. We illustrate the mechanism by analytically studying spin models with the Glauber-typed dynamics under periodic perturbations. Then, we show that the scenario is supported by numerical simulations of mean-field as well as two-dimensional spin systems.Comment: 6 pages, 5 figure

Residual discrete symmetry of the five-state clock model

It is well-known that the $q$-state clock model can exhibit a Kosterlitz-Thouless (KT) transition if $q$ is equal to or greater than a certain threshold, which has been believed to be five. However, recent numerical studies indicate that helicity modulus does not vanish in the high-temperature phase of the five-state clock model as predicted by the KT scenario. By performing Monte Carlo calculations under the fluctuating twist boundary condition, we show that it is because the five-state clock model does not have the fully continuous U(1) symmetry even in the high-temperature phase while the six-state clock model does. We suggest that the upper transition of the five-state clock model is actually a weaker cousin of the KT transition so that it is $q \ge 6$ that exhibits the genuine KT behavior.Comment: 13 pages, 17 figure

Surface-Enhanced Raman Spectroscopy (SERS) Based on ZnO Nanorods for Biological Applications

Detection of nanometer-sized biomarkers is a research topic that attracts much attention as an application for early diagnosis of diseases. Biopsy monitoring by analyzing cell secretion in a non-destructive way has many advantages in the field of biomedicine. We introduce the Raman signal enhancement method on a biosensing chip based on surface-enhanced Raman diagnosis. This approach has the advantage because the ZnO nanorods are grown to form nanoscale porosity and are coated with gold to enable size selective biomarker detection. After sputtering gold on the grown ZnO nanostructures, the unique feature of clustering the nanorod’s heads first appeared. The grain formation on the head was the main factor for the localized surface plasmon resonance (LSPR) enhancement, and this fact could be verified by finite element analysis. It has been demonstrated in breast cancer cell line that the cell viability is also high in such gold-clad ZnO nanostructure-based surface-enhanced substrates. For bioapplication, interstitial cystitis/bladder pain syndrome (IC/BPS) animal model was prepared by injecting HCl into the bladder of a rat, and urine was collected a week later to conduct Raman spectroscopy experiments