Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.00432 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913359127904256 |
|---|---|
| author | Luck, Jean-Marc |
| author_facet | Luck, Jean-Marc |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00432 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting log-periodic oscillations Luck, Jean-Marc Statistical Mechanics 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. |
| title | Revisiting log-periodic oscillations |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2403.00432 |