Polymers on disordered trees, spin glasses, and traveling waves

B. Derrida, H. Spohn

Research output: Contribution to journalArticlepeer-review

392 Scopus citations


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.

Original languageEnglish
Pages (from-to)817-840
Number of pages24
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Jun 1988
Externally publishedYes


  • Disordered system
  • freezing transition
  • reaction-diffusion equation
  • spin glass


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