Revisiting log-periodic oscillations

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.

• Publication year

  2024

• Venue

  Physica A: Statistical Mechanics and its Applications

• Publication date

  2024-03-01

• Fields of study

  Physics

• Identifiers
  DOI 10.1016/j.physa.2024.129821arXiv 2403.00432
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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