37th M. Smoluchowski Symposium on Statistical Physics

Restoring the Fluctuation–Dissipation Theorem in phase transition through a New Emergent Fractal Dimension

17 Sept 2024, 15:00

40m

Faculty of Physics, Astronomy and Applied Computer Science; Jagiellonian University

Invited talk Session 6

Speaker

Fernando Oliveira (Universidade de Brasília)

Description

We develop a hypothesis that the dynamics of equilibrium systems at criticality have their dynamics constricted to a fractal subspace. We relate the correlation fractal dimension associated with this subspace to the Fisher critical exponent controlling the singularity associated with the correlation function. This fractal subspace is different from that which is associated with the order parameter. We propose a relation between the correlation fractal dimension and the order parameter fractal dimension. The fractal subspace we identify has as a defining property that the correlation function is restored at the critical point by restricting the dynamics this way[1]. We determine the correlation fractal dimension of the 2d Ising model and validate it by computer simulations. We discuss growth models briefly in this context[2].

[1] MS Gomes-Filho, P de Castro, DB Liarte, FA Oliveira
Entropy 26 (3), 260 (2024)

[2] Henrique A Lima, Edwin E Mozo Luis, Ismael SS Carrasco, Alex Hansen, Fernando A Oliveira, arXiv preprint arXiv:2402.10167