Abstract
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 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 ( d e f ), which plays the role of the Euclidean dimension in the formulation of the dynamic scaling and in the hyperscaling relationship d e f = 2 β / 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Physica A: Statistical Mechanics and its Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
