Topological Effects caused by the Fractal Substrate on the Nonequilibrium Critical Behavior of the Ising Magnet

M.A.BAB; G.FABRICIUS; E.V.ALBANO

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

The American Physical Society

Año: 2006 vol. 74 p. 41123 - 4112310

1063-651X

The nonequilibrium critical dynamics of the Ising magnet on a fractal substrate, namely the Sierpinski carpetwith Hausdorff dimension dH=1.7925, has been studied within the short-time regime by means of Monte Carlosimulations. The evolution of the physical observables was followed at criticality, after both annealing orderedspin configurations
ground state and quenching disordered initial configurations
high temperature state, forthree segmentation steps of the fractal. We have obtained evidence showing that during these relaxationprocesses both the growth and the fragmentation of magnetic domains become influenced by the hierarchicalstructure of the substrate. In fact, the interplay between the dynamic behavior of the magnet and the underlyingfractal leads to the emergence of a logarithmic-periodic oscillation, superimposed to a power law, which hasbeen 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 thesecond-order phase transition and the critical exponents corresponding to the short-time regime. The effects ofthe substrate can also be observed from the dependence of the effective critical exponents on the segmentationstep. The exponent
of the initial increase of the magnetization has also been obtained and the results suggestthat it would be almost independent of the fractal dimension of the susbstrate, provided that dH is close enoughto d=2. The oscillations have been discussed within the framework of the discrete scale invariance of thesubstrate.