Critical Exponents of the Ising Model on Low Dimensional Fractal Media

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

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER

Año: 2009 vol. 388 p. 370 - 378

0378-4371

The critical behavior of the Ising model on fractal substrates with noninteger Hausdorff dimension d_H<2 and infinite ramification order is studied by means of the short-time critical dynamic scaling approach. Our determinations of the critical temperatures and critical exponents eta, gamma, and u are compared to the predictions of the Wilson-Fisher expansion, the Wallace-Zia expansion, the transfer matrix method, and more recent Monte Carlo simulations using finite-size scaling analysis. We also determined the effective dimension (d_{ef}), which plays the role of the Euclidean dimension in the formulation of the dynamic scaling and in the hyperscaling relationship d_{ef}=2\beta /nu +gamma / nu. Furthermore, we obtained the dynamic exponent z of the nonequilibriun correlation length and the exponent theta that governs the initial increase of the magnetization. Our results are consistent with the convergence of the lower-critical dimension towards d=1 for fractal substrates and suggest that the Hausdorff dimension may be different from the effective dimension.