Scaling Invariance: A Gateway to Phase Transitions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912316628402176 |
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| author | Leonel, Edson D. |
| author_facet | Leonel, Edson D. |
| contents | We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in the phase space. The key variables are the action and the angle, as usual from Hamiltonian systems. The transition is influenced by a control parameter giving the form of the order parameter. We observe a scaling invariance in the average squared action within the chaotic region, providing evidence that this change from regularity (integrability) to chaos (non-integrability) is akin to a second-order or continuous phase transition. As the order parameter approaches zero, its response against the variation of the control parameter (susceptibility) becomes increasingly pronounced (indeed diverging), resembling a phase transition. These findings could not be obtained without a seminal paper on Phys. Rev. Lett. {\bf 2004}, {\em 93}, 014101. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling Invariance: A Gateway to Phase Transitions Leonel, Edson D. Chaotic Dynamics We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in the phase space. The key variables are the action and the angle, as usual from Hamiltonian systems. The transition is influenced by a control parameter giving the form of the order parameter. We observe a scaling invariance in the average squared action within the chaotic region, providing evidence that this change from regularity (integrability) to chaos (non-integrability) is akin to a second-order or continuous phase transition. As the order parameter approaches zero, its response against the variation of the control parameter (susceptibility) becomes increasingly pronounced (indeed diverging), resembling a phase transition. These findings could not be obtained without a seminal paper on Phys. Rev. Lett. {\bf 2004}, {\em 93}, 014101. |
| title | Scaling Invariance: A Gateway to Phase Transitions |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2504.06187 |