Revisiting log-periodic oscillations

Jean-Marc Luck

Physica A: Statistical Mechanics and its Applications, 2024, vol. 643, issue C

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.

Keywords: Log-periodic oscillations; Oscillatory critical amplitudes; Fragmentation models; Finite-size scaling; Non-linear recursions; Discrete scale invariance (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:643:y:2024:i:c:s0378437124003303

DOI: 10.1016/j.physa.2024.129821

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