Speaker
Description
The fluctuation-dissipation theorem is the main tool for obtaining the response of a physical system. However, FDT fails in many situations (see [1] for review), such as phase transitions, spin glass, anomalous diffusion, and growth phenomena. We develop the hypothesis that the dynamics of a given system may lead to a fractal dimension $d_f$ 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 dimensionality. We discuss how this phenomenon appears in phase transition and growth phenomena [2-7]. We show that the Fisher exponent $\eta$
$$η = d − df $$ is the deviation from the integer dimension. Thus we determine exactly the fractal dimension df for the Ising model in two dimensions as $d_f = 7/4$ and we validate it via computer simulations.
[1] MS Gomes-Filho, L Lapas, E Gudowska-Nowak, FA Oliveira Physics Reports 1141, 1-43 (2025).
[2] M. Kardar, Statistical physics of fields (Cambridge University Press, 2007)
[3] HA Lima, EEM Luis, ISS Carrasco, A Hansen, FA Oliveira Physical
Review E 110, L062107 (2024).
[4] M. S. Gomes-Filho, A. L. A. Penna and F. A. Oliveira, Results in Physics
26, 104435 (2021).
[5] E. E. M. Luis, T. A. de Assis, F. A. Oliveira, Journal of Statistical Mechanics: Theory and Experiment 8, 083202 (2022).
[6] E. E. Mozo Luis, F. A. Oliveira, and T. A. de Assis, Phys. Rev. E 107,
034802 (2023).
[7] MS Gomes-Filho, P de Castro, DB Liarte, FA Oliveira Entropy 26 (3),
260 (2024).
