Journal of Statistical Physics

, Volume 45, Issue 3–4, pp 439–449 | Cite as

Exactly solvable one-dimensional inhomogeneous models

  • B. Derrida
  • M. Mendès France
  • J. Peyrière


We present a simple way of constructing one-dimensional inhomogeneous models (random or quasiperiodic) which can be solved exactly. We treat the example of an Ising chain in a varying magnetic field, but our procedure can easily be extended to other one-dimensional inhomogeneous models. For all the models we can construct, the free energy and its derivatives with respect to temperature can be computed exactly at one particular temperature.

Key words

Liapunov exponent Ising chain disordered chain quasiperiodic chain exactly solvable model 


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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • B. Derrida
    • 1
  • M. Mendès France
    • 2
  • J. Peyrière
    • 3
  1. 1.Service de Physique ThéoriqueCEN SaclayGif sur YvetteFrance
  2. 2.Département de Mathématiques et InformatiqueUniversité de Bordeaux 1TalenceFrance
  3. 3.Département de MathématiquesUniversité de Paris-SudOrsayFrance

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