2,412 research outputs found
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 -state clock model can exhibit a
Kosterlitz-Thouless (KT) transition if 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 that exhibits the genuine KT behavior.Comment: 13 pages, 17 figure
Estimation of object location probability for object detection using brightness feature only
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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