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2018 Dynamical freezing in a spin glass system with logarithmic correlations
Aser Cortines, Julian Gold, Oren Louidor
Electron. J. Probab. 23: 1-31 (2018). DOI: 10.1214/18-EJP181


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.


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Aser Cortines. Julian Gold. Oren Louidor. "Dynamical freezing in a spin glass system with logarithmic correlations." Electron. J. Probab. 23 1 - 31, 2018.


Received: 26 November 2017; Accepted: 23 May 2018; Published: 2018
First available in Project Euclid: 11 June 2018

zbMATH: 06924671
MathSciNet: MR3814253
Digital Object Identifier: 10.1214/18-EJP181

Primary: 60G15, 60G57, 60G70, 60K37, 82C44, 82D30


Vol.23 • 2018
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