Search results for "Dimension"
showing 10 items of 2766 documents
Ising Spin-Glass on a Lattice with Small Loops
1991
We consider the Ising spin-glass on a special lattice containing small loops with finite coordination number c. We derive the equation for the effective field distribution. With zero external field, we calculate the spin-glass transition temperature and obtain the lower critical dimension of the system. We investigate the system near and below the spin-glass transition and find that the replica symmetric solution is unstable in the low-temperature phase. Our results indicate that the replica symmetry breaking (RSB) effects are stronger than that of the Bethe lattice and furthermore, RSB is enhanced as the dimension (c/2) is decreased. Comparison with recent results of the 1/d expansion is a…
Spin stiffness of vector spin glasses
2011
Abstract We study domain-wall excitations for O ( m ) vector spin glasses in the limit m → ∞ , where the energy landscape is simplified considerably compared to XY or Heisenberg models due to the complete disappearance of metastability. Using numerical ground-state calculations and appropriate pairs of complementary boundary conditions, domain-wall defects are inserted into the systems and their excitation energies are measured. This allows us to determine the stiffness exponents for lattices of a range of spatial dimensions d = 2 , … , 7 . Compiling these results, we can finally determine the lower critical dimension of the model. The outcome is compared to estimates resulting from field-t…
Monte Carlo study of the bimodal three-state Potts glass
1992
Employing Monte Carlo simulations, we compute the spin-glass susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{SG}}$(T) of the three-state Potts glass model on a simple-cubic lattice for various temperatures and lattice sizes ranging from L=4 to 10. We use the discrete \ifmmode\pm\else\textpm\fi{}J distribution for the bonds. Comparing our results with a recent high-temperature series expansion, we find a systematic deviation at lower temperatures, which cannot be explained by finite-size effects in our data. The low-temperature behavior of ${\mathrm{\ensuremath{\chi}}}_{\mathrm{SG}}$(T) is compatible with d = 3 being the lower critical dimension of this model.
On the ambiguities of sign determination of the S-matrix from energy levels in a finite box
2013
In a recent paper the authors make a study on the determination of the S-matrix elements for scattering of particles in the infinite volume from the energy levels in a finite box for the case of multiple channels. The study is done with a toy model in 1+1 dimension and the authors find that there is some ambiguity in the sign of nondiagonal matrix elements, casting doubts on whether the needed observables in the infinite volume can be obtained from the energy levels of the box. In this paper I present an easy derivation, confirming the ambiguity of the sign and argue that this, however, does not put restrictions in the determination of observables.
Surface tension and interfacial fluctuations in d-dimensional Ising model
2005
The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d-1)…
Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
1999
Monte Carlo results for the moments of the magnetization distribution of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L (4 \leq L \leq 22) is the linear dimension of a hypercubic lattice with periodic boundary conditions in d=5 dimensions, are analyzed in the critical region and compared to a recent theory of Chen and Dohm (CD) [X.S. Chen and V. Dohm, Int. J. Mod. Phys. C (1998)]. We show that this finite-size scaling theory (formulated in terms of two scaling variables) can account for the longstanding discrepancies between Monte Carlo results and the so-called ``lowest-mode'' theory, which uses a single scaling variable tL^{d/2} where t=T/T_c-1 is the temperature distan…
Self-consistent calculation of the flux-flow conductivity in diffusive superconductors
2017
In the framework of Keldysh-Usadel kinetic theory, we study the temperature dependence of flux-flow conductivity (FFC) in diffusive superconductors. By using self-consistent vortex solutions we find the exact values of dimensionless parameters that determine the diffusion-controlled FFC both in the limit of the low temperatures and close to the critical one. Taking into account the electron-phonon scattering we study the transition between flux-flow regimes controlled either by the diffusion or the inelastic relaxation of non-equilibrium quasiparticles. We demonstrate that the inelastic electron-phonon relaxation leads to the strong suppression of FFC as compared to the previous estimates m…
To the theory of high-power gyrotrons with uptapered resonators
2010
In high-power gyrotrons it is desirable to combine an optimal resonator length with the optimal value of the resonator quality factor. In resonators with the constant radius of the central part, the possibilities of this combination are limited because the quality factor of the resonator sharply increases with its length. Therefore the attempts to increase the length for maximizing the efficiency leads to such increase in the quality factor which makes the optimal current too small. Resonators with slightly uptapered profiles offer more flexibility in this regard. In such resonators, one can separate optimization of the interaction length from optimization of the quality factor because the …
3D reconstruction of external and internal surfaces of transparent objects from polarization state of highlights
2014
A vision-based method is proposed to measure the 3D shape of external and internal surfaces (not accessible) of smooth transparent objects. Looking at the reflections of point sources on a specular surface with a polarimetric camera, we combine the measurements of two techniques: shape from distortion and shape from polarization. It permits us to recover the position and orientation of the specular surface for each detected point. The internal surface of transparent objects exhibiting as well a specular component, the same technique is used on the highlights coming from the back surface, taking into account the refraction by using polarimetric ray tracing.
Universal extra dimensions andZ→bb¯
2003
We study, at the one loop level, the dominant contributions from a single universal extra dimension to the process $\stackrel{\ensuremath{\rightarrow}}{Z}b\overline{b}.$ By resorting to the gaugeless limit of the theory we explain why the result is expected to display a strong dependence on the mass of the top quark, not identified in the early literature. A detailed calculation corroborates this expectation, giving rise to a lower bound for the compactification scale which is comparable to that obtained from the $\ensuremath{\rho}$ parameter. An estimate of the subleading corrections is furnished, together with a qualitative discussion on the difference between the present results and thos…