Radiation Pressure Induced Instabilities in Laser Interferometric Detectors of Gravitational Waves

The large scale interferometric gravitational wave detectors consist of Fabry-Perot cavities operating at very high powers ranging from tens of kW to MW for next generations. The high powers may result in several nonlinear effects which would affect the performance of the detector. In this paper, we investigate the effects of radiation pressure, which tend to displace the mirrors from their resonant position resulting in the detuning of the cavity. We observe a remarkable effect, namely, that the freely hanging mirrors gain energy continuously and swing with increasing amplitude. It is found that the `time delay', that is, the time taken for the field to adjust to its instantaneous equilibrium value, when the mirrors are in motion, is responsible for this effect. This effect is likely to be important in the optimal operation of the full-scale interferometers such as VIRGO and LIGO.Comment: 27 pages, 11 figures, RevTex styl

Scaling law of Wolff cluster surface energy

We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension $1 < d_f \le 3$ in the framework of the Ising model. The mean absolute value of the surface energy of Wolff cluster follows a power law with respect to the lattice size. Moreover, we investigate the probability density distribution of the surface energy of Wolff cluster and are able to establish a new scaling relation. It enables us to introduce a new exponent associated to the surface energy of Wolff cluster. Finally, this new exponent is linked to a dynamical exponent via an inequality.Comment: 12 pages, 3 figures. To appear in PR

Unique gap structure and symmetry of the charge density wave in single-layer VSe2_2

Single layers of transition metal dichalcogenides (TMDCs) are excellent candidates for electronic applications beyond the graphene platform; many of them exhibit novel properties including charge density waves (CDWs) and magnetic ordering. CDWs in these single layers are generally a planar projection of the corresponding bulk CDWs because of the quasi-two-dimensional nature of TMDCs; a different CDW symmetry is unexpected. We report herein the successful creation of pristine single-layer VSe$_2$, which shows a ($\sqrt7 \times \sqrt3$) CDW in contrast to the (4 $\times$ 4) CDW for the layers in bulk VSe$_2$. Angle-resolved photoemission spectroscopy (ARPES) from the single layer shows a sizable ($\sqrt7 \times \sqrt3$) CDW gap of $\sim$100 meV at the zone boundary, a 220 K CDW transition temperature twice the bulk value, and no ferromagnetic exchange splitting as predicted by theory. This robust CDW with an exotic broken symmetry as the ground state is explained via a first-principles analysis. The results illustrate a unique CDW phenomenon in the two-dimensional limit

Critical behavior of the 3-state Potts model on Sierpinski carpet

We study the critical behavior of the 3-state Potts model, where the spins are located at the centers of the occupied squares of the deterministic Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo simulations, for a Hausdorff dimension $d_{f}$ $\simeq 1.8928$. The phase transition is shown to be a second order one. The maxima of the susceptibility of the order parameter follow a power law in a very reliable way, which enables us to calculate the ratio of the exponents $\gamma /\nu$. We find that the scaling corrections affect the behavior of most of the thermodynamical quantities. However, the sequence of intersection points extracted from the Binder's cumulant provides bounds for the critical temperature. We are able to give the bounds for the exponent $1/\nu$ as well as for the ratio of the exponents $\beta/\nu$, which are compatible with the results calculated from the hyperscaling relation.Comment: 13 pages, 4 figure

Critical Behavior of the Ferromagnetic Ising Model on a Sierpinski Carpet: Monte Carlo Renormalization Group Study

We perform a Monte Carlo Renormalization Group analysis of the critical behavior of the ferromagnetic Ising model on a Sierpi\'nski fractal with Hausdorff dimension $d_f\simeq 1.8928$. This method is shown to be relevant to the calculation of the critical temperature $T_c$ and the magnetic eigen-exponent $y_h$ on such structures. On the other hand, scaling corrections hinder the calculation of the temperature eigen-exponent $y_t$. At last, the results are shown to be consistent with a finite size scaling analysis.Comment: 16 pages, 7 figure