### Abstract

Original language | English |
---|---|

Pages (from-to) | 125203 |

Number of pages | 1 |

Journal | Journal of Mathematical Physics |

Volume | 49 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 2008 |

### Fingerprint

### Keywords

- phase transformations
- free energy
- polymer structure
- polymers

### Cite this

*Journal of Mathematical Physics*,

*49*(12), 125203. https://doi.org/10.1063/1.2962981

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 49, no. 12, pp. 125203. https://doi.org/10.1063/1.2962981

}

TY - JOUR

T1 - Minimal supporting subtrees for the free energy of polymers on disordered trees

AU - Morters, Peter

AU - Ortgiese, Marcel

PY - 2008/12

Y1 - 2008/12

N2 - 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.

AB - 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.

KW - phase transformations

KW - free energy

KW - polymer structure

KW - polymers

UR - http://www.scopus.com/inward/record.url?scp=58149242807&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1063/1.2962981

U2 - 10.1063/1.2962981

DO - 10.1063/1.2962981

M3 - Article

VL - 49

SP - 125203

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

ER -