Search results for "Exponent"
showing 10 items of 896 documents
Kinetics of the Formation of Ordered Domains on Surfaces: Theoretical Considerations and Monte-Carlo Simulation
1986
When an adsorbed monolayer which initially is in a disordered state is suddenly brought to a temperature in the regime of the ordered phase, domains of the ordered phase are predicted to form and grow with time t after the quench according to a power law, i.e. linear dimension L(t) ∞ tx. At the same time, the structure function S(k,t) is predicted to satisfy a scaling law, S(k,t) = S(k,tx), k being the difference between the wave vector observed in the scattering and the Bragg wave vector describing the long range order. The theoretical ideas which lead to this behaviour are briefly reviewed, and evidence from simulations of simple lattice gas models and Potts models is presented. Particula…
Critical and tricritical singularities of the three-dimensional random-bond Potts model for large $q$
2005
We study the effect of varying strength, $\delta$, of bond randomness on the phase transition of the three-dimensional Potts model for large $q$. The cooperative behavior of the system is determined by large correlated domains in which the spins points into the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder $\delta>\delta_t$ this percolating cluster coexists with a percolating cluster of non-correlated spins. Such a co-existence is only possible in more than two dimensions. We argue and check numerically that $\delta_t$ is the tricritical disorder, which se…
Computer simulation of models for orientational glasses
1991
Abstract Monte Carlo studies of two- and three-dimensional lattice models where quadrupoles interact with a nearest-neighbor Gaussian coupling are reviewed. None of these models has a thermodynamic glass phase transition at non-zero temperature like the Ising spin glass: rather, phase transitions at zero temperature occur that exhibit a dynamical freeze-in spread out over a wide temperature range and are characterized by a strongly non-exponential relaxation. The time-dependent glass order parameter, q(t), decays with time, t, compatible with a stretched exponential decay q(t) ∼ exp [− (t/τ)y] with a strongly temperature-dependent exponent. While the static glass ‘susceptibility’ for isotro…
DIELECTRIC AGEING IN LAYERED FERROELECTRICS
2008
ABSTRACT Studies of the effects of sample history on long-term relaxation of polarization in the Na0.5Bi8.5Ti2Nb4O27 and Na0.5Bi8.5Ti2Ta4O27 ferroelectrics of layered structures are reported. The type of functional relationship of e′(t) at measuring procedures including heating or cooling to the temperature being examined Ta is found to change from exponential (Kohlrausch function) to logarithmic. Results are discussed within the assumption of presence of defect complexes in disordered ferroelectrics.
Quantum Critical Scaling under Periodic Driving
2016
Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model's microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time $\tau_{bd}$, proportional to the size of the system. This behavio…
Energy fluctuations and the singularity of specific heat in a 3D Ising model
2004
We study the energy fluctuations in 3D Ising model near the phase transition point. Specific heat is a relevant quantity which is directly related to the mean squared amplitude of the energy fluctuations in the system. We have made extensive Monte Carlo simulations in 3D Ising model to clarify the character of the singularity of the specific heat C v based on the finite-size scaling of its maximal values C v max depending on the linear size of the lattice L . An original iterative method has been used which automatically finds the pseudocritical temperature corresponding to the maximum of C v . The simulations made up to L ≤ 128 with application of the Wolff's cluster algorithm allowed us t…
Critical Phenomena at the Surface of Systems Undergoing a Bulk First Order Transition: Are They Understood?
2002
Systems that exhibit a first-order phase transition in the bulk, such as binary alloys where the order parameter vanishes discontinuously at some critical value of a control parameter, may show a continuous vanishing of the local order parameter at the surface. This “surface-induced disordering” is described theoretically as a variant of critical wetting, where an interface between the locally disordered surface and the ordered bulk gradually moves towards the bulk. We test this description by Monte Carlo simulations for a body centered cubic model alloy, with interactions between nearest and next nearest neighbors, for which the phase diagram in the bulk has been calculated very accurately…
Critical wetting in the square Ising model with a boundary field
1990
The Ising square lattice with nearest-neighbor exchangeJ>0 and a free surface at which a boundary magnetic fieldH1 acts has a second-order wetting transition. We study the surface excess magnetization and the susceptibility ofL×M lattices by Monte Carlo simulation and probe the critical behavior of this wetting transition, applying finite-size scaling methods. For the cases studied, the results are not consistent with the presumably exactly known values of the critical exponents, because the asymptotic critical region has not yet been reached. Implication of our results for critical wetting in three dimensions and for the application of the present model to adsorbed wetting layers at surfac…
Polymer mixtures in confined geometries: Model systems to explore phase transitions
2005
While binary (A,B) symmetric polymer mixtures ind = 3 dimensions have an unmixing critical point that belongs to the 3d Ising universality class and crosses over to mean field behavior for very long chains, the critical behavior of mixtures confined into thin film geometry falls in the 2d Ising class irrespective of chain length. The critical temperature always scales linearly with chain length, except for strictly two-dimensional chains confined to a plane, for whichT; c ∝N; 5/8 (this unusual exponent describes the fractal contact line between segregated chains in dense melts in two spatial dimensions, d = 2). When the walls of the thin film are not neutral, but preferentially attract one …
Time-resolved coherent anti-Stokes Raman-scattering measurements of I2 in solid Kr: vibrational dephasing on the ground electronic state at 2.6-32 K.
2005
Time-resolved coherent anti-Stokes Raman-scattering (CARS) measurements are carried out for iodine (I2) in solid krypton matrices. The dependence of vibrational dephasing time on temperature and vibrational quantum number v is studied. The v dependence is approximately quadratic, while the temperature dependence of both vibrational dephasing and spectral shift, although weak, fits the exponential form characteristic of dephasing by pseudolocal phonons. The analysis of the data indicates that the frequency of the pseudolocal phonons is approximately 30 cm(-1). The longest dephasing times are observed for v = 2 being approximately 300 ps and limited by inhomogeneous broadening. An increase in…