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}
}
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… 
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