Searcharxiv⌕ Search

arXiv subjects

D. P. Landau

Publications and source records attributed to D. P. Landau.

43 records · Page 3Linked to original sources
arXiv1999

Spin dynamics simulation of the three-dimensional XY model: Structure factor and transport properties

We present extensive Monte-Carlo spin dynamics simulations of the classical XY model in three dimensions on a simple cubic lattice with periodic boundary conditions. A recently developed efficient integration algorithm for the equations of motion is used, which allows a substantial improvement of statistics and large integration times. We find spin wave peaks in a wide range around the critical point and spin diffusion for all temperatures. At the critical point we find evidence for a violation of dynamic scaling in the sense that independent components of the dynamic structure factor S(q,w) require different dynamic exponents in order to obtain scaling. Below the critical point we investigate the dispersion relation of the spin waves and the linewidths of S(q,w) and find agreement with mode coupling theory. Apart from strong spin wave peaks we observe additional peaks in S(q,w) which can be attributed to two-spin wave interactions. The overall lineshapes are also discussed and compared to mode coupling predictions. Finally, we present first results for the transport coefficient D(q,w) of the out-of-plane magnetization component at the critical point, which is related to the thermal conductivity of He4 near the superfluid-normal transition.

cond-mat.stat-mech↗
arXiv1998

Fast spin dynamics algorithms for classical spin systems

We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion used in Molecular Dynamics these algorithms are based on the Suzuki-Trotter decomposition of exponential operators and unlike more commonly used algorithms exactly conserve spin length and, in special cases, energy. Using higher order decompositions we investigate integration schemes of up to fourth order and compare them to a well established fourth order predictor-corrector method. We demonstrate that these methods can be used with much larger time steps than the predictor-corrector method and thus may lead to a substantial speedup of computer simulations of the dynamical behavior of magnetic materials.

cond-mat.stat-mech↗
arXiv1997

Temperature dependent correlation length for the S=1/2 Quantum Heisenberg Antiferromagnet on the square lattice

We present an analysis of high precision Monte Carlo data for the two dimensional S=1/2 quantum Heisenberg antiferromagnet up to $ξ= 95.7(3)$ obtained by the continuous time version of the loop algorithm. Our data are in good agreement with a prediction of the recent theory (Phys. Rev. Lett. vol. 77, 3439 (1996)) in very high temperature regime, but they strongly disagree with it in the low temperature regime.

cond-mat.stat-mech↗
arXiv1996

Critical dynamics in the 2d classical XY-model: a spin dynamics study

Using spin-dynamics techniques we have performed large-scale computer simulations of the dynamic behavior of the classical three component XY-model (i.e. the anisotropic limit of an easy-plane Heisenberg ferromagnet), on square lattices of size up to 192^2, for several temperatures below, at, and above T_KT. The temporal evolution of spin configurations was determined numerically from coupled equations of motion for individual spins by a fourth order predictor-corrector method, with initial spin configurations generated by a hybrid Monte Carlo algorithm. The neutron scattering function S(q,omega) was calculated from the resultant space-time displaced spin-spin correlation function. Pronounced spin-wave peaks were found both in the in-plane and the out-of-plane scattering function over a wide range of temperatures. The in-plane scattering function S^xx also has a large number of clear but weak additional peaks, which we interpret to come from two-spin-wave scattering. In addition, we observed a small central peak in S^xx, even at temperatures well below the phase transition. We used dynamic finite size scaling theory to extract the dynamic critical exponent z. We find z=1.00(4) for all T <= T_KT, in excellent agreement with theoretical predictions, although the shape of S(q,omega) is not well described by current theory.

cond-mat↗
arXiv1996

Numerical Computation of Finite Size Scaling Functions: An Alternative Approach to Finite Size Scaling

Using single cluster flip Monte Carlo simulations we accurately determine new finite size scaling functions which are expressed only in terms the variable $x = ξ_L / L$, where $ξ_L$ is the correlation length in a finite system of size $L$. Data for the d=2 and d=3 Ising models, taken at different temperatures and for different size lattices, show excellent data collapse over the entire range of scaling variable for susceptibility and correlation length. From these finite size scaling functions we can estimate critical temperatures and exponents with rather high accuracy even though data are not obtained extremely close to the critical point. The bulk values of the renormalized four-point coupling constant are accurately measured and show strong evidence for hyperscaling.

cond-mat↗
arXiv1994

Universal order-parameter profiles for critical adsorption and the extraordinary transition: a comparison of epsilon-expansion and Monte Carlo results

The universal, scaled order parameter profiles $P_{\pm}(z/ξ)$ for critical adsorption of a fluid or fluid mixture onto a wall or interface, and for the extraordinary transition of the semi-infinite Ising model, are discussed theoretically, where $z$ is the distance from the interface, $ξ(T)$ is the bulk correlation length, and the subscript $+$ ($-$) refers to the approach from above (below) $T_c$. Recent results to first order in the $ε=4-d$ expansion are extrapolated to $d=3$ space dimensions and compared with new Monte Carlo results. In order to obtain meaningful extrapolations it is crucial that both the exponential decay at large $ζ$ as well as the known algebraic behavior $P_{\pm}(ζ)\simζ^{-β/ν}$ at small $ζ$ be correctly reproduced. To this end a recently developed novel RG scheme involving a $z$ dependent amplitude renormalization is used. Reasonable agreement of our extrapolations with the Monte Carlo results and some experimental results is obtained.

cond-mat↗