# Directed Polymers on Hierarchical Lattices with site disorder.

Abstract : We study a polymer model on hierarchical lattices very close to the one introduced and studied in papers by Derrida and Griffith, and by Cook and Derrida. For this model, we prove the existence of free energy and derive the necessary and sufficient condition for which very strong disorder holds for all $\beta$, and give some accurate results on the behavior of the free energy at high-temperature. We obtain these results by using a combination of fractional moment method and change of measure over the environment to obtain an upper bound, and second moment method to get a lower bound. We also get lower bounds on the fluctuation exponent of $\log Z_n$, and study the infinite polymer measure in the weak disorder phase.
Keywords :
Document type :
Preprints, Working Papers, ...
2009
Domain :

https://hal.archives-ouvertes.fr/hal-00391412
Contributor : Gregorio Moreno Flores <>
Submitted on : Thursday, June 4, 2009 - 9:06:38 AM
Last modification on : Wednesday, October 12, 2016 - 1:04:16 AM
Document(s) archivé(s) le : Friday, June 11, 2010 - 12:18:26 AM

### Files

HDPS0406.pdf
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### Identifiers

• HAL Id : hal-00391412, version 1
• ARXIV : 0906.0992

### Citation

Hubert Lacoin, Gregorio Moreno Flores. Directed Polymers on Hierarchical Lattices with site disorder.. 2009. <hal-00391412>

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