Polymers on disordered trees, spin glasses, and traveling waves

Polymers on disordered trees, spin glasses, and traveling waves

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...

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Bibliographic Details
Published in:Journal of statistical physics Vol. 51; no. 5-6; pp. 817 - 840
Main Authors: Derrida, B., Spohn, H.
Format: Journal Article
Language:English
Published: Springer Verlag 01-06-1988
Subjects:
Physics
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Summary: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.
ISSN:0022-4715
1572-9613
DOI:10.1007/BF01014886