Phase transition-like behavior in a low-pass filter

Hubert Krivine (1) , Annick Lesne (2)

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
2 LPTL - Laboratoire de Physique Théorique des Liquides

We discuss an iterative electric circuit for which the limits of infinite number of elements and zero dissipation in each element do not commute. The circuit is taken from the Feynman lectures, where it was argued on physical considerations that an infinite circuit made only of inductances and capacitances would behave as a dissipative system with nonvanishing resistance below a threshold frequency. The understanding of this behavior requires that the two limits be taken in the appropriate order. This simple example illustrates that caution in multiple limiting procedures is necessary to obtain the correct physical behavior. A close analogy with the standard ferromagnetic transition of the Ising model is drawn. ©2003 American Association of Physics Teachers.

Hubert Krivine, Annick Lesne. Phase transition-like behavior in a low-pass filter. American Journal of Physics, 2003, 71, pp.31-33. ⟨10.1119/1.1514233⟩. ⟨hal-00012073⟩