2,412 research outputs found

    Percolation on hyperbolic lattices

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    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

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    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

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    It is well-known that the qq-state clock model can exhibit a Kosterlitz-Thouless (KT) transition if qq 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≥6q \ge 6 that exhibits the genuine KT behavior.Comment: 13 pages, 17 figure

    Estimation of object location probability for object detection using brightness feature only

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    Most existing object detection methods use features such as color, shape, and contour. If there are no consistent features can be used, we need a new object detection method. Therefore, in this paper, we propose a new method for estimating the probability that an object can be located for object detection and generating an object location probability map using only brightness in a gray image. To evaluate the performance of the proposed method, we applied it to gallbladder detection. Experimental results showed 98.02% success rate for gallbladder detection in ultrasonogram. Therefore, the proposed method accurately estimates the object location probability and effectively detected gallbladder
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