Alberto Sicilia

Kibble-Zurek mechanism and infinitely slow annealing through critical points

We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phase ordering systems during an infinitely slow annealing across a second-order phase transition. We elucidate the time and cooling rate dependence of the typical growing length, and we use it to predict the number of topological defects left over in the symmetry broken phase as a function of time, both close and far from the critical region. Our results extend the Kibble-Zurek mechanism and reveal its limitations.

Curvature-driven coarsening in the two-dimensional Potts model

We study the geometric properties of polymixtures after a sudden quench in temperature. We mimic these systems with the q -states Potts model on a square lattice with and without weak quenched disorder, and their evolution with Monte Carlo simulations with nonconserved order parameter. We analyze the distribution of hull-enclosed areas for different initial conditions and compare our results with recent exact and numerical findings for q=2 (Ising) case. Our results demonstrate the memory of the presence or absence of long-range correlations in the initial state during the coarsening regime and exhibit superuniversality properties.

Experimental Test of Curvature-Driven Dynamics in the Phase Ordering of a Two Dimensional Liquid Crystal

We study electric field driven deracemization in an achiral liquid crystal through the formation and coarsening of chiral domains. It is proposed that deracemization in this system is a curvature-driven process. We test this prediction using the recently obtained exact result for the distribution of hull-enclosed areas in two-dimensional coarsening with nonconserved scalar order parameter dynamics [J. J. Arenzon et al., Phys. Rev. Lett. 98, 145701 (2007)]. The experimental data are in very good agreement with the theory. We thus demonstrate that deracemization in such bent-core liquid crystals belongs to the Allen-Cahn universality class, and that the exact formula, which gives us the statistics of domain sizes during coarsening, can also be used as a strict test for this dynamic universality class.

Geometrical properties of parafermionic spin models

We present measurements of the fractal dimensions associated with the spin clusters for Z4 and Z5 spin models. We also attempted to measure similar fractal dimensions for the generalized Fortuin–Kastelyn clusters in these models, but we discovered that these clusters do not percolate at the critical point of the model under consideration. These results clearly mark a difference in behavior of these non-local objects as compared to the Ising model or the three-state Potts model, which correspond to the simplest cases of ZN spin models with N = 2 and N = 3 respectively. We compare these fractal dimensions with the ones obtained for SLE interfaces.

Coarsening in the Potts model: out-of-equilibrium geometric properties

Geometric properties of polymixtures after a sudden quench in temperature are studied through the q-states Potts model on a square lattice, and their evolution with Monte Carlo simulations with non-conserved order parameter. We analyse the distribution of hull enclosed areas for different initial conditions and compare with exact and numerical findings for the q = 2 (Ising) case.

Domain growth in 2d: exact results, simulations and experiments

We obtain the exact distribution of the areas enclosed by domain boundaries (‘hulls’) during the coarsening dynamics of a two‐dimensional nonconserved scalar field. This result represents the first analytical demostration of the dynamical scaling hypothesis for this system. The experimental data for the formation of chiral domains in liquid crystals are in very good agreement with the theory.