Dynamical freezing in a spin glass system with logarithmic correlations

Aser Cortines, Julian Gold, Oren Louidor

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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 limit as a spatial K-process driven by a random trapping landscape, which is explicitly related to the limiting extremal process of the field. Alternatively, the limiting process is a supercritical Liouville Brownian motion with respect to the continuum Gaussian free field on the box. This demonstrates rigorously and for the first time, as far as we know, a dynamical freezing in a spin glass system with logarithmically correlated energy levels.

Original languageEnglish (US)
Article number59
JournalElectronic Journal of Probability
Volume23
DOIs
StatePublished - 2018

Keywords

  • Aging
  • Dynamical freezing
  • Gaussian free field
  • K-process
  • Random walk in a random potential
  • Spin-glasses
  • Trap models

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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