Fluctuations of the partition function in the generalized random energy model with external field
We study Derrida's generalized random energy model (GREM) in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic ...
We study Derrida's generalized random energy model (GREM) in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic ...
A remark on the infinite-volume Gibbs measures of spin glasses
In this note, we point out that infinite-volume Gibbs measures of spin glass models on the hypercube can be identified as random probability measures on the unit ball of a Hilbert space. This simple o...
In this note, we point out that infinite-volume Gibbs measures of spin glass models on the hypercube can be identified as random probability measures on the unit ball of a Hilbert space. This simple o...
Minimal supporting subtrees for the free energy of polymers on disordered trees
J. Math. Phys. 49, 125203 (2008); doi:10.1063/1.2962981
Published 4 December 2008
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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.
©2008 American Institute of Physics
| History: | Received 30 May 2008; accepted 26 June 2008; published 4 December 2008 |
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