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

Peter Morters, Marcel Ortgiese

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)125203
Number of pages1
JournalJournal of Mathematical Physics
Volume49
Issue number12
DOIs
Publication statusPublished - Dec 2008

Fingerprint

Critical value
Free Energy
Polymers
free energy
Martingale Method
Branching Random Walk
Directed Polymers
Decrease
Random Trees
Weight Distribution
polymers
Exponential Growth
martingales
Identically distributed
Disorder
Phase Transition
Strictly
random walk
apexes
Zero

Keywords

  • phase transformations
  • free energy
  • polymer structure
  • polymers

Cite this

Minimal supporting subtrees for the free energy of polymers on disordered trees. / Morters, Peter; Ortgiese, Marcel.

In: Journal of Mathematical Physics, Vol. 49, No. 12, 12.2008, p. 125203.

Research output: Contribution to journalArticle

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