Journal of Statistical Physics

, Volume 51, Issue 5–6, pp 817–840 | Cite as

Polymers on disordered trees, spin glasses, and traveling waves

  • B. Derrida
  • H. Spohn


We show that the problem of a directed polymer on a tree with disorder can be reduced to the study of nonlinear equations of reaction-diffusion type. These equations admit traveling wave solutions that move at all possible speeds above a certain minimal speed. The speed of the wavefront is the free energy of the polymer problem and the minimal speed corresponds to a phase transition to a glassy phase similar to the spin-glass phase. Several properties of the polymer problem can be extracted from the correspondence with the traveling wave: probability distribution of the free energy, overlaps, etc.

Key words

Disordered system spin glass freezing transition reaction-diffusion equation 


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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • B. Derrida
    • 1
  • H. Spohn
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of CaliforniaSanta Barbara

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