Dynamical Freezing in a Spin Glass System with Logarithmic Correlations

@article{Cortines2017DynamicalFI,
  title={Dynamical Freezing in a Spin Glass System with Logarithmic Correlations},
  author={A. A. G. Cortines and Julian Gold and Oren Louidor},
  journal={arXiv: Probability},
  year={2017}
}
We consider a continuous time random walk on the two-dimensional discrete torus, whose motion is governed by the discrete Gaussian free field on the corresponding box acting as a potential. More precisely, at any vertex the walk waits an exponentially distributed time with mean given by the exponential of the field and then jumps to one of its neighbors, chosen uniformly at random. We prove that throughout the low-temperature regime and at in-equilibrium timescales, the process admits a scaling… 
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