One step replica symmetry breaking and extreme order statistics of logarithmic REMs

@article{Cao2016OneSR,
  title={One step replica symmetry breaking and extreme order statistics of logarithmic REMs},
  author={Xiangyu Cao and Yan V. Fyodorov and Pierre Le Doussal},
  journal={arXiv: Statistical Mechanics},
  year={2016}
}
Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models (logREMs) behave in the thermodynamic limit as a randomly shifted decorated exponential Poisson point process. The distribution of the random shift is determined solely by the large-distance ("infra-red", IR) limit of the model, and is equal to the free energy… 

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