Revisiting log-periodic oscillations
arXiv:2403.00432 · doi:10.1016/j.physa.2024.129821
Abstract
This work is inspired by a recent study of a two-dimensional stochastic fragmentation model. We show that the configurational entropy of this model exhibits log-periodic oscillations as a function of the sample size, by exploiting an exact recursion relation for the numbers of its jammed configurations. This is seemingly the first statistical-mechanical model where log-periodic oscillations affect the size dependence of an extensive quantity. We then propose and investigate in great depth a one-dimensional analogue of the fragmentation model. This one-dimensional model possesses a critical point, separating a strong-coupling phase where the free energy is super-extensive from a weak-coupling one where the free energy is extensive and exhibits log-periodic oscillations. This model is generalized to a family of one-dimensional models with two integer parameters, which exhibit essentially the same phenomenology.
26 pages, 13 figures, 2 tables