Critical Exponents of the Ising Model on Low Dimensional Fractal Media.

A. BAB, M.; GABRIEL FABRICIUS,; EZEQUIEL V ALBANO

Physica A - Statistical and Theoretical Physics

Elsevier

Lugar: Amstrerdam; Año: 2009 vol. 338 p. 370 - 378

0378-4371

The critical behavior of the Ising model on fractal substrates with noninteger Hausdorffdimension dH < 2 and infinite ramification order is studied by means of the shorttimecritical dynamic scaling approach. Our determinations of the critical temperaturesand critical exponents ,  , and are compared to the predictions of the WilsonFisherexpansion, the WallaceZia expansion, the transfer matrix method, and more recent MonteCarlo simulations using finite-size scaling analysis. We also determined the effectivedimension (def ), which plays the role of the Euclidean dimension in the formulation of thedynamic scaling and in the hyperscaling relationship def D 2= C  =. Furthermore,we obtained the dynamic exponent z of the nonequilibrium correlation length and theexponent that governs the initial increase of the magnetization. Our results are consistentwith the convergence of the lower-critical dimension towards d D 1 for fractal substrates