Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time

M.BAB; G.FABRICIUS; E.ALBANO

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

Año: 2005 vol. 71 p. 36139 - 36147

1063-651X

The short-time dynamic evolution of an Ising model embedded in an infinitely ramified fractal structure with noninteger Hausdorff dimension was studied using Monte Carlo simulations. Completely ordered and disordered spin configurations were used as initial states for the dynamic simulations. In both cases, the evolution of the physical observables follows a power-law behavior. Based on this fact, the complete set of critical exponents characteristic of a second-order phase transition was evaluated. Also, the dynamic exponent uof the critical initial increase in magnetization, as well as the critical temperature, were computed. The exponent u critical initial increase in magnetization, as well as the critical temperature, were computed. The exponent u uof the critical initial increase in magnetization, as well as the critical temperature, were computed. The exponent uu exhibits a weak dependence on the initial ssmalld magnetization. On the other hand, the dynamic exponent zssmalld magnetization. On the other hand, the dynamic exponent z shows a systematic decrease when the segmentation step is increased, i.e., when the system size becomes larger. Our results suggest that the effective noninteger dimension for the second-order phase transition is noticeably smaller than the Hausdorff dimension. Even when the behavior of the magnetization sin the case of the ordered initial stated and the autocorrelation sin the case of the disordered initial stated with time are very well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale. well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale. the ordered initial stated and the autocorrelation sin the case of the disordered initial stated with time are very well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale. well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale. sin the case of the ordered initial stated and the autocorrelation sin the case of the disordered initial stated with time are very well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale. well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale. d and the autocorrelation sin the case of the disordered initial stated with time are very well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale.