Título: Restoring the fluctuation-dissipation theorem in growth and phase transition through a new emergent fractal dimension
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Palestrante: Prof. Dr. Fernando Albuquerque Oliveira (UNB)

 

 

Resumo: We develop the hypothesis that the dynamics of a given system may lead to a fractal dimension df different from the original spatial dimension d. This phenomenon is more easy to observe near a phase transition. We also speculate how the response function might be sensitive to this change in di- mensionality. We discuss how this phenomenon appears in phase transition and growth phenomena. Furthermore, we show that correlations appear as the difference between d − df becomes sensitive[1], an effect similar to what occurs in growth phenomena[2-3]. Moreover, we determine[1] the Fisher exponent as η = d − df , and the fractal dimension df for the Ising model. We validate it via computer simulations for two dimensions[1].
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[1] H. A. Lima, E. E. M. Luis, I. S. S. Carrasco, A. Hansen, F. A. Oliveira. Physical Review E 110, L062107, arXiv preprint arXiv:2402.10167 .

[2] P. R. H. dos Anjos, W. S. Alves, M. S. Gomes-Filho, D. L. Azevedo and F. A. Oliveira, Frontiers in Physics 9 , 741590 (2021).

[3] M. S. Gomes-Filho, Pablo de Castro, D. B. Liarte, and F. A. Oliveira, Entropy, 26, 260 (2024). https://www.mdpi.com/1099-4300/26/3/260