Critical exponents of the Ising model on low-dimensional fractal media

M.A. Bab, G. Fabricius and E.V. Albano

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 4, 370-378

Abstract: The critical behavior of the Ising model on fractal substrates with noninteger Hausdorff dimension dH<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 β, γ, and ν 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 (def), which plays the role of the Euclidean dimension in the formulation of the dynamic scaling and in the hyperscaling relationship def=2β/ν+γ/ν. Furthermore, we obtained the dynamic exponent z of the nonequilibrium correlation length and the exponent θ 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.

Keywords: Ising model; Fractal media; Critical behavior; Monte Carlo method; Out equilibrium physics (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437108008789
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:4:p:370-378

DOI: 10.1016/j.physa.2008.10.029

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().