# 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}
}
• Published 3 November 2017
• Mathematics
• arXiv: Probability
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…
Asymptotic behavior of a low temperature non-cascading 2-GREM dynamics at extreme time scales
• Physics
• 2020
We derive the scaling limit for the Hierarchical Random Hopping dynamics for the non cascading 2-GREM at low temperatures and time scales where the dynamics is close to equilibrium. The fine tuning
Extrema of the Two-Dimensional Discrete Gaussian Free Field
• M. Biskup
• Mathematics
Springer Proceedings in Mathematics & Statistics
• 2019
These lecture notes offer a gentle introduction to the two-dimensional Discrete Gaussian Free Field with particular attention paid to the scaling limits of the level sets at heights proportional to
Infinite Level GREM-Like K-Processes Existence and Convergence
• Mathematics
• 2021
We derive the existence of infinite level GREM-like K-processes by taking the limit of a sequence of finite level versions of such processes as the number of levels diverges. The main step in the
Tightness of Liouville first passage percolation for γ ∈ ( 0 , 2 ) $\gamma \in (0,2)$
• Mathematics
• 2019
We study Liouville first passage percolation metrics associated to a Gaussian free field h $h$ mollified by the two-dimensional heat kernel p t $p_{t}$ in the bulk, and related star-scale invariant
Heat Kernel for Liouville Brownian Motion and Liouville Graph Distance
• Mathematics
Communications in Mathematical Physics
• 2019
We show the existence of the scaling exponent $$\chi = \chi (\gamma )$$χ=χ(γ), with \begin{aligned} 0 < \chi \le \frac{4}{\gamma ^2} \left( \left( 1+ {\gamma ^2} / 4 \right) - \sqrt{1+ {\gamma ^4}

## References

SHOWING 1-10 OF 36 REFERENCES
Glass transition of a particle in a random potential, front selection in nonlinear renormalization group, and entropic phenomena in Liouville and sinh-Gordon models.
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2001
Applications to Dirac fermions in random magnetic fields at criticality reveal a peculiar "quasilocalized" regime (corresponding to the glass phase for the particle), where eigenfunctions are concentrated over a finite number of distant regions, and allow us to recover the multifractal spectrum in the delocalized regime.
Freezing of dynamical exponents in low dimensional random media.
• Physics
Physical review letters
• 2001
A particle in a random potential with logarithmic correlations in dimensions d = 1,2 is shown to undergo a dynamical transition at T(dyn)>0, and anomalous scaling occurs in the creep dynamics, relevant to dislocation motion experiments.
Glass transition of a particle in a random potential, front selection in nonlinear RG and entropic phenomena in Liouville and SinhGordon models
• Physics
• 2000
We study via RG, numerics, exact bounds and qualitative arguments the equilibrium Gibbs measure of a particle in a $d$-dimensional gaussian random potential with {\it translationally invariant
Communications in Mathematical Physics Glauber Dynamics of the Random Energy Model I . Metastable Motion on the Extreme States ∗
• Mathematics
We investigate the long-time behavior of the Glauber dynamics for the random energy model below the critical temperature. We give very precise estimates on the motion of the process to and between
Communications in Mathematical Physics Glauber Dynamics of the Random Energy Model II . Aging Below the Critical Temperature ∗
• Mathematics
• 2003
We investigate the long-time behavior of the Glauber dynamics for the random energy model below the critical temperature. We establish that for a suitably chosen timescale that diverges with the size
Glauber Dynamics of the Random Energy Model
• Mathematics
• 2003
Abstract: We investigate the long-time behavior of the Glauber dynamics for the random energy model below the critical temperature. We give very precise estimates on the motion of the process to and
Glauber Dynamics of the Random Energy Model
• Mathematics
• 2003
Abstract: We investigate the long-time behavior of the Glauber dynamics for the random energy model below the critical temperature. We establish that for a suitably chosen timescale that diverges
Liouville Brownian Motion at Criticality
• Mathematics
• 2013
In this paper, we construct the Brownian motion of Liouville Quantum Gravity with central charge c=1 (more precisely we restrict to the corresponding free field theory). Liouville quantum gravity
Extremes of the discrete two-dimensional Gaussian free field
We consider the lattice version of the free field in two dimensions and study the fractal structure of the sets where the field is unusually high (or low). We then extend some of our computations to