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Scaling Invariance: A Gateway to Phase Transitions
1Departamento de Física, Universidade Estadual Paulista (UNESP), Av. 24A, 1515, São Paulo 13506-900, SP, Brazil.
Abstract:
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from regularity to 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 in the control parameter (susceptibility) becomes increasingly pronounced (indeed diverging), resembling a phase transition.
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