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American Journal of Physics -- January 2003 -- Volume 71, Issue 1, pp. 31

Phase transition-like behavior in a low-pass filter

H. Krivine1 and A. Lesne2

1Laboratoire de Physique Théorique et Modèles Statistiques, Bât. 100, 91405 Orsay Cedex, France
2Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, Case Courrier 121, 4 Place Jussieu, 75252 Paris Cedex 05, France

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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.

© 2003 American Association of Physics Teachers

EDITORIALLY RELATED

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    Jack L. Uretsky
    Am. J. Phys. 71, 1320 (2003)AJPIAS000071000012001320000001
  2. Comment on "Phase transition-like behavior in a low-pass filter," by H. Krivine and A. Lesne [Am. J. Phys. 71 (1), 31–33 (2003)]
    A. Lesne
    Am. J. Phys. 71, 732 (2003)AJPIAS000071000007000732000002

KEYWORDS and PACS

Keywords

circuit theory, low-pass filters, bifurcation, Ising model, critical phenomena, phase transformations, recursion method

PACS

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History
Received Mar 2002
Accepted Aug 2002
Online Dec 2002

PUBLICATION DATA

ISSN

0002-9505 (print)  

Publisher

$abstract.society.value is a Member of CrossRef American Association of Physics Teachers

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1119/1.1514233

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