Growth of order in vector spin systems; scaling and universality

Ferromagnetism-induced phase separation in a two-dimensional spin fluid

We study the liquid-gas phase separation observed in a system of repulsive particles dressed with ferromagnetically aligning spins, a so-called "spin fluid." Microcanonical ensemble numerical simulations of finite-size systems reveal that magnetization sets in and induces a liquid-gas phase separation between a disordered gas and a ferromagnetic dense phase at low enough energies and large enough densities. The dynamics after a quench into the coexistence region show that the order parameter associated with the liquid-vapor phase separation follows an algebraic law with an unusual exponent, as it is forced to synchronize with the growth of the magnetization: this suggests that for finite size systems the magnetization sets in along a Curie line, which is also the gas-side spinodal line, and that the coexistence region ends at a tricritical point. This picture is confirmed at the mean-field level with different approximation schemes, namely, a Bethe lattice resolution and a virial expansion complemented by the introduction of a self-consistent Weiss-like molecular field. However, a detailed finite-size scaling analysis shows that in two dimensions the ferromagnetic phase escapes the Berezinskii-Kosterlitz-Thouless scenario and that the long-range order is not destroyed by the unbinding of topological defects. The Curie line thus becomes a magnetic crossover in the thermodynamic limit. Finally, the effects of the magnetic interaction range and those of the interaction softness are characterized within a mean-field semianalytical low-density approach.

Generic features of the fluctuation dissipation relation in coarsening systems

The integrated response function in phase-ordering systems with scalar, vector, conserved, and nonconserved order parameter is studied at various space dimensionalities. Assuming scaling of the aging contribution chi(ag) (t, t(w) )= tw (- a(chi) ) chi; (t/ t(w) ) we obtain, by numerical simulations and analytical arguments, the phenomenological formula describing the dimensionality dependence of a(chi) in all cases considered. The primary result is that a(chi) vanishes continuously as d approaches the lower critical dimensionality d(L). This implies that (i) the existence of a nontrivial fluctuation dissipation relation and (ii) the failure of the connection between statics and dynamics are generic features of phase ordering at d(L).

Corrections to scaling in the phase-ordering dynamics of a vector order parameter

Corrections to scaling, associated with deviations of the order parameter from the scaling morphology in the initial state, are studied for systems with O(n) symmetry at zero temperature in phase-ordering kinetics. Including corrections to scaling, the equal time pair correlation function has the form C(r,t)=f0(r/L)+L(-omega)f1(r/L)+., where L is the coarsening length scale. The correction-to-scaling exponent omega and the correction-to-scaling function f1(x) are calculated for both nonconserved and conserved order parameter systems using the approximate Gaussian closure theory of Mazenko. In general omega is a nontrivial exponent which depends on both the dimensionality d of the system and the number of components n of the order parameter. Corrections to scaling are also calculated for the nonconserved one-dimensional XY model, where an exact solution is possible.

Dynamical scaling: the two-dimensional XY model following a quench

To sensitively test scaling in the two-dimensional 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 approximately (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 nontopological "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.