• DOI:10.1063/1.2962982
• Corpus ID: 16870771

Fluctuations of the partition function in the generalized random energy model with external field

@article{Bovier2008FluctuationsOT,
  title={Fluctuations of the partition function in the generalized random energy model with external field},
  author={Anton Bovier and Anton Klimovsky},
  journal={Journal of Mathematical Physics},
  year={2008},
  volume={49},
  pages={125202}
}

• A. Bovier, A. Klimovsky
• Published 10 May 2008
• Mathematics
• Journal of Mathematical Physics

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 limit for all admissible values of parameters. We find that the fluctuations are described by a hierarchical structure which is obtained by a certain coarse graining of the initial hierarchical structure of the GREM with external field. We provide an explicit formula for the free energy of the model. We also derive some large deviation results providing an expression for the free energy in a class of models with Gaussian Hamiltonians and external field. Finally, we prove that the coarse-grained parts of the system emerging in the thermodynamic limit tend to have a certain optimal magnetization, as prescribed by the strength of the external field and by parameters of the GREM.