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Article Dans Une Revue Physica A: Statistical Mechanics and its Applications Année : 2024

Revisiting log-periodic oscillations

Résumé

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.
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Dates et versions

hal-04584649 , version 1 (23-05-2024)

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Citer

Jean-Marc Luck. Revisiting log-periodic oscillations. Physica A: Statistical Mechanics and its Applications, 2024, 643, pp.129821. ⟨10.1016/j.physa.2024.129821⟩. ⟨hal-04584649⟩
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