Search results for "Exponent"

High-temperature series expansion for the relaxation times of the two dimensional Ising model

1995

We derive the high temperature series expansions for the two relaxation times of the single spin-flip kinetic Ising model on the square lattice. The series for the linear relaxation time τl is obtained with 20 non-trivial terms, and the analysis yields 2.183±0.005 as the value of the critical exponentΔl, which is equal to the dynamical critical exponentz in the two-dimensional case. For the non-linear relaxation time we obtain 15 non-trivial terms, and the analysis leads to the resultsΔnl = 2.08 ± 0.07. The scaling relationΔl −Δnl = β (β being the exponent of the order parameter) seems to be fulfilled, though the error bars ofΔnl are still quite substantial. In addition, we obtain the serie…

Interface localization transition in Ising films with competing walls: Ginzburg criterion and crossover scaling.

1996

Antiferromagnetic Heisenberg chains with bond alternation and quenched disorder

2004

We consider S=1/2 antiferromagnetic Heisenberg chains with alternating bonds and quenched disorder, which represents a theoretical model of the compound CuCl_{2x}Br_{2(1-x)}(\gamma-{pic})_2. Using a numerical implementation of the strong disorder renormalization group method we study the low-energy properties of the system as a function of the concentration, x, and the type of correlations in the disorder. For perfect correlation of disorder the system is in the random dimer (Griffiths) phase having a concentration dependent dynamical exponent. For weak or vanishing disorder correlations the system is in the random singlet phase, in which the dynamical exponent is formally infinity. We disc…

Importance of the crossover-current density for a vortex-glass analysis

2000

Recent experimental results obtained from transport measurements on extremely long measurement bridges [1] have questioned the validity of previous vortex-glass analyses. For electric-field windows restricted to relatively high values of E > 10 -5 V/m the dynamic exponent of the vortex-glass transition z 6, in agreement with theoretical predictions and previous experimental results. However, for extended windows (10 -1 > E > 10 -8 V/m) - while the characteristics of a vortex-glass transition are preserved - all analyses result in z ≥ 9. A combined analysis of the crossover-current density J + 0 and crossover-electric field E + 0 , which limit the critical regime of the vortex-glass transiti…

Effects of surface nonlinear interactions on the local critical behavior

1987

Effects of surface nonlinear interactions on the local critical behaviors are studied for an-component field in the semi-infinite space near the SB (surface-bulk) point by using renormalization group methods. The model Hamiltonian consists of a free (Gaussian) bulk part and a surface term containing aφ4 interaction. The interplay between the free bulk term and the nonlinear surface term gives rise to interesting behaviors of the local surface properties. Whereas the local susceptibility and correlation exponents retain their mean-field values, the surface crossover exponent ϕ is non-mean-field below three dimensions. To second order in e(e=3−d) we find:η‖ and\(\phi = \frac{1}{2} - \frac{{n …

Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture II: Intermediate Scattering Function and Dynamic Susceptibility

1995

We have performed a molecular dynamics computer simulation of a supercooled binary Lennard-Jones system in order to compare the dynamical behavior of this system with the predictions of the idealized version of mode-coupling theory (MCT). By scaling the time $t$ by the temperature dependent $\alpha$-relaxation time $\tau(T)$, we find that in the $\alpha$-relaxation regime $F(q,t)$ and $F_s(q,t)$, the coherent and incoherent intermediate scattering functions, for different temperatures each follows a $q$-dependent master curve as a function of scaled time. We show that during the early part of the $\alpha$-relaxation, which is equivalent to the late part of the $\beta$-relaxation, these mast…

Nonmonotonical crossover of the effective susceptibility exponent

1997

We have numerically determined the behavior of the magnetic susceptibility upon approach of the critical point in two-dimensional spin systems with an interaction range that was varied over nearly two orders of magnitude. The full crossover from classical to Ising-like critical behavior, spanning several decades in the reduced temperature, could be observed. Our results convincingly show that the effective susceptibility exponent gamma_eff changes nonmonotonically from its classical to its Ising value when approaching the critical point in the ordered phase. In the disordered phase the behavior is monotonic. Furthermore the hypothesis that the crossover function is universal is supported.

Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules

1997

Using molecular dynamics computer simulations, we investigate the dynamics of the rotational degrees of freedom in a supercooled system composed of rigid, diatomic molecules. The interaction between the molecules is given by the sum of interaction-site potentials of the Lennard-Jones type. In agreement with mode-coupling theory (MCT), we find that the relaxation times of the orientational time correlation functions C_1^(s), C_2^(s) and C_1 show at low temperatures a power-law with the same critical temperature T_c, and which is also identical to the critical temperature for the translational degrees of freedom. In contrast to MCT we find, however, that for these correlators the time-tempera…

Linear inverse filtering improves spatial separation of nonlinear brain dynamics: a simulation study.

2000

We examined topographic variations in nonlinear measures based on scalp voltages, which were generated by two simulated current dipoles each placed in a different hemisphere of a spherical volume conductor (three-shell model). Dipole dynamics were that of a three-torus and the x-component of the Lorenz-system and scalp voltage were calculated for a configuration of 29 electrode positions. Although estimates for correlation dimension D2 and Lyapunov exponent L1 were close to the theoretical values for the original time series, the simulated scalp voltage data showed almost no topographic resolution of dipole positions. In order to enhance topographic differentiation, we constructed linear in…

Monte Carlo simulation of dimensional crossover in the XY model.

1993

We report Monte Carlo simulations of Villain's periodic Gaussian XY model on ${\mathit{L}}^{2}$\ifmmode\times\else\texttimes\fi{}N lattices of film geometry (L\ensuremath{\gg}N) with up to N=16 layers, employing the single-cluster update algorithm combined with improved estimators for measurements. The boundary conditions are periodic within each layer and free at the bottom and top layer. Based on data for the specific heat, the spin-spin correlation function, and the susceptibility in the high-temperature phase we study the crossover from three- to two-dimensional behavior as criticality is approached. For the transition temperatures, determined from Kosterlitz-Thouless fits to the correl…