Directed Polymers on Hierarchical Lattices with site disorder

Details Directed Polymers on Hierarchical Lattices with site disorder Directed Polymers on Hierarchical Lattices with site disorder

2009-06-04

arxiv.org/abs/0906.0992v1

Mathematics

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We study a polymer model on hierarchical lattices very close to the one introduced and studied in \cite{DGr, CD}. 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 $\gb$, 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.

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