arXiv subjects

F. Rojas

Publications and source records attributed to F. Rojas.

21 records · Page 2Linked to original sources

arXiv1999

Dynamical Scaling: the Two-Dimensional XY Model Following a Quench

To sensitively test scaling in the 2D XY model quenched from high-temperatures into the ordered phase, we study the difference between measured correlations and the (scaling) results of a Gaussian-closure approximation. We also directly compare various length-scales. All of our results are consistent with dynamical scaling and an asymptotic growth law $L \sim (t/\ln[t/t_0])^{1/2}$, though with a time-scale $t_0$ that depends on the length-scale in question. We then reconstruct correlations from the minimal-energy configuration consistent with the vortex positions, and find them significantly different from the ``natural'' correlations --- though both scale with $L$. This indicates that both topological (vortex) and non-topological (``spin-wave'') contributions to correlations are relevant arbitrarily late after the quench. We also present a consistent definition of dynamical scaling applicable more generally, and emphasize how to generalize our approach to other quenched systems where dynamical scaling is in question. Our approach directly applies to planar liquid-crystal systems.

cond-mat.stat-mech↗

arXiv1996

Structure-Factor Tail for the Ordering Kinetics of Nonconserved Fields without Topological Defects

Using a cell dynamic system (CDS) simulation scheme, we investigate the phase-ordering dynamics of non-conserved O(n) models without topological defects, i.e. for $n > d+1$ where $d$ is the spatial dimensionality. In particular, we consider zero-temperature quenches for $d=2$, $n=4,5$, and for $d=1$, $n=3,4,5$. We find, in agreement with previous simulations using fixed-length spins, that dynamical scaling is obtained, with characteristic length $L(t) = t^{1/2}$. We show that the asymptotic behaviour of the structure-factor scaling function $g(q)$ is well fitted by the stretched exponential form $g(q)\sim \exp(-bq^δ)$, with an exponent $δ$ that appears to depend on both n and d. An analytical treatment of an approximate large-N equation for the pair correlation function yields $g(q) \sim q^{-(d-1)/2}\exp(-bq)$, with $b \sim (\ln n)^{1/2}$ for large $n$, in agreement with recent simulations of the same equation.

cond-mat↗

arXiv1995

Ordering Kinetics of Conserved XY Models

The zero-temperature ordering kinetics of conserved XY models in spatial dimensions $d=2$ and 3 is studied using cell dynamical simulations. The growth of the characteristic length scale $L(t)$ is fully consistent with recent theoretical predictions: $L(t) \sim t^{1/4}$ for $d=2$ and $L(t) \sim (t\ln t)^{1/4}$ for $d=3$. A gaussian closure approximation describes the form of the structure factor rather well for $d=3$.

cond-mat↗