Minimal supporting subtrees for the free energy of polymers on disordered trees


Morters, P. and Ortgiese, M., 2008. Minimal supporting subtrees for the free energy of polymers on disordered trees. Journal of Mathematical Physics, 49 (12), p. 125203.

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We consider a model of directed polymers on a regular tree with a disorder given by independent, identically distributed weights attached to the vertices. For suitable weight distributions this model undergoes a phase transition with respect to its localization behavior. We show that, for high temperatures, the free energy is supported by a random tree of positive exponential growth rate, which is strictly smaller than that of the full tree. The growth rate of the minimal supporting subtree decreases to zero as the temperature decreases to the critical value. At the critical value and all lower temperatures, a single polymer suffices to support the free energy. Our proofs rely on elegant martingale methods adapted from the theory of branching random walks.


Item Type Articles
CreatorsMorters, P.and Ortgiese, M.
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Uncontrolled Keywordsphase transformations,free energy,polymer structure,polymers
DepartmentsFaculty of Science > Mathematical Sciences
Research CentresCentre for Mathematical Biology
ID Code12523


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