Phase ordering in 3D XY and Ising models: slow growth, Mpemba effect and experimental relevance.

We study phase ordering dynamics in the three-dimensional nonconserved XY model, via Monte Carlo simulations, for quenches from the paramagnetic phase to certain final temperatures Tf within the ferromagnetic region of the phase diagram. The growth in the system occurs via annihilation of vortex and anti-vortex pairs. In the three dimensional system geometry, the cores of these vortices join from different planes on which the spins lie, forming line defects. In the long-time limit, the associated characteristic length scale, ℓ(t), appears to grow with time (t) approximately as t0.15 for Tf = 0, as estimated from an analysis of the time-dependent exponent. Like in the zero temperature intermediate time ordering in the three dimensional Ising model, the exponent is much smaller than 1/2, the expected value that is realized for quenches to a Tf value that is larger than zero. We carry out quenches from different starting temperatures, Ts, that lie above the critical temperature Tc. It is observed that the systems with higher Ts approach the final equilibrium faster. This resembles the puzzling Mpemba effect, which we could not detect in the 2D XY model. We also present similar results from simulations of the two- and three-dimensional Ising model. In the case of the 2D Ising model, we could detect the Mpemba effect only when the starting magnetization is restricted to a value close to zero. In space dimension d = 3, on the other hand, the effect was detected for both models even if the initial configurations at a given Ts are chosen from the full distribution of magnetization. Thus, our results are of much experimental relevance.