Dicrete Scale Invaiance Effects in the Non-Equilibrium Critical Behavior of the Ising Magnet on Fractal Substrate.

M BAB,; GABRIEL FABRICIUS,; EZEQUIEL V ALBANO

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

APS

Lugar: Ridge, New York; Año: 2006 vol. 74 p. 41123 - 10000000

1063-651X

The nonequilibrium critical dynamics of the Ising magnet on a fractal substrate, namely the Sierpinski carpet with Hausdorff dimension dH=1.7925, has been studied within the short-time regime by means of Monte Carlo simulations. The evolution of the physical observables was followed at criticality, after both annealing ordered spin configurations (ground state) and quenching disordered initial configurations (high temperature state), for three segmentation steps of the fractal. We have obtained evidence showing that during these relaxation processes both the growth and the fragmentation of magnetic domains become influenced by the hierarchical structure of the substrate. In fact, the interplay between the dynamic behavior of the magnet and the underlying fractal leads to the emergence of a logarithmic-periodic oscillation, superimposed to a power law, which has been observed in the time dependence of both the decay of the magnetization and its logarithmic derivative. These oscillations have been carefully characterized in order to determine the critical temperature of the second-order phase transition and the critical exponents corresponding to the short-time regime. The effects of the substrate can also be observed from the dependence of the effective critical exponents on the segmentation step. The exponent q of the initial increase of the magnetization has also been obtained and the results suggest that it would be almost independent of the fractal dimension of the substrate, provided that dHis close enough to d=2. The oscillations have been discussed within the framework of the discrete scale invariance of the substrate.