Search results for "Exponent"
showing 10 items of 896 documents
Surface critical behaviour near the uniaxial Lifshitz point of the axial next-nearest-neighbour Ising model
1999
The semi-infinite axial next-nearest-neighbour Ising (ANNNI) model in the disordered phase is treated within a molecular-field approximation, and the singularities of various response functions characterizing the critical behaviour at the surface are obtained. In previous work (Binder K and Frisch H L 1999 Eur. Phys. J. B 10 71) the axis where a nearest-neighbour ferromagnetic (J 1 ) and next-nearest-neighbour antiferromagnetic (J 2 ) exchange compete was chosen perpendicular to the surface plane. In the present work we consider an orientation of this axis parallel to the surface, allowing also for different values of these exchange interactions (j 1 ,j 2 ) in the surface plane. We derive t…
Memory effects in the relaxation of the Gaussian trap model
2011
We investigate the memory effect in a simple model for glassy relaxation, a trap model with a Gaussian density of states. In this model thermal equilibrium is reached at all finite temperatures and therefore we can consider jumps from low to high temperatures in addition to the quenches usually considered in aging studies. We show that the evolution of the energy following the Kovacs-protocol can approximately be expressed as a difference of two monotonously decaying functions and thus show the existence of a so-called Kovacs hump whenever these functions are not single exponentials. It is well established that the Kovacs effect also occurs in the linear response regime and we show that mos…
Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange : A Monte Carlo study
1998
,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor ±Ĵ-interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (T/Ĵ ≥ 0.6). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function…
Absence of hyperscaling violations for phase transitions with positive specific heat exponent
1994
Finite size scaling theory and hyperscaling are analyzed in the ensemble limit which differs from the finite size scaling limit. Different scaling limits are discussed. Hyperscaling relations are related to the identification of thermodynamics as the infinite volume limit of statistical mechanics. This identification combined with finite ensemble scaling leads to the conclusion that hyperscaling relations cannot be violated for phase transitions with strictly positive specific heat exponent. The ensemble limit allows to derive analytical expressions for the universal part of the finite size scaling functions at the critical point. The analytical expressions are given in terms of generalH-fu…
Correlation and Spectral Properties of Vehicle-to-Vehicle Channels in the Presence of Moving Scatterers
2013
This paper derives a vehicle-to-vehicle (V2V) channel model assuming a typical propagation scenario in which the local scatterers move with random velocities in random directions. The complex channel gain of the proposed V2V channel model is provided. Subsequently, for different scatterer velocity distributions, the corresponding autocorrelation function (ACF), power spectral density (PSD), and the Doppler spread of the channel are derived, shown, and confirmed by the available measurement data. It is shown that the Gaussian mixture (GM) and the exponential distribution can accurately describe the velocity distribution of relatively fast and slow moving scatterers, respectively. Since the p…
A method of evaluation of measured light intensities and degrees of polarization of a unit volume of turbid air
1965
In order to interpret scattered light measurements a comparison with theoretical values is necessary. It is demonstrated by means of an example the possibility to obtain a first view on the measurement results. From calculated values of various aerosol size distribution models as well as from measurements were computed: 1) the angular quotients of scattered light intensity (i.e., quotients of intensity at two scattering angles and the same wavelength) and 2) the wavelength quotients (i.e., quotients of intensity at two wavelengths and the same scattering angle). The comparison between measured and theoretical values informs us of the exponent of the aerosol size distribution and its boundar…
Finite-size scaling approach for critical wetting: rationalization in terms of a bulk transition with an order parameter exponent equal to zero.
2012
Clarification of critical wetting with short-range forces by simulations has been hampered by the lack of accurate methods to locate where the transition occurs. We solve this problem by developing an anisotropic finite-size scaling approach and show that then the wetting transition is a ``bulk'' critical phenomenon with order parameter exponent equal to zero. For the Ising model in two dimensions, known exact results are straightforwardly reproduced. In three dimensions, it is shown that previous estimates for the location of the transition need revision, but the conclusions about a slow crossover away from mean-field behavior remain unaltered.
Multicanonical Monte Carlo study and analysis of tails for the order-parameter distribution of the two-dimensional Ising model.
2003
The tails of the critical order-parameter distribution of the two-dimensional Ising model are investigated through extensive multicanonical Monte Carlo simulations. Results for fixed boundary conditions are reported here, and compared with known results for periodic boundary conditions. Clear numerical evidence for ‘‘fat’’ stretched exponential tails exists below the critical temperature, indicating the possible presence of fat tails at the critical temperature. Our work suggests that the true order-parameter distribution at the critical temperature must be considered to be unknown at present.
Thermodynamics of the two-dimensional Heisenberg classical honeycomb lattice
1998
In this article we adapt a previous work concerning the two-dimensional (2D) Heisenberg classical square lattice [Physica B 245, 263 (1998)] to the case of a honeycomb lattice. Closed-form expressions of the main thermodynamic functions of interest are derived in the zero-field limit. Notably, near absolute zero (i.e., the critical temperature), we derive the values of the critical exponents $\ensuremath{\alpha}=0,\ensuremath{\eta}=\ensuremath{-}1,\ensuremath{\gamma}=3,$ and $\ensuremath{\nu}=1,$ as for the square lattice, thus proving their universal character. A very simple model allows one to give a good description of the low-temperature behaviors of the product $\ensuremath{\chi}T.$ Fo…
The Peregrine breather of order nine and its deformations with sixteen parameters solutions to the NLS equation
2015
Abstract We construct new deformations of the Peregrine breather ( P 9 ) of order 9 with 16 real parameters. With this method, we obtain explicitly new families of quasi-rational solutions to the NLS equation in terms of a product of an exponential depending on t by a ratio of two polynomials of degree 90 in x and t; when all the parameters are equal to 0, we recover the classical P 9 breather. We construct new patterns of different types of rogue waves as triangular configurations of 45 peaks as well as rings and concentric rings.