Dynamical Freezing in a Spin Glass System with Logarithmic Correlations

Vortrag von Dr. Aser Cortines Peixoto

Datum: 28.02.18  Zeit: 17.15 - 19.00  Raum: Y27H12

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 neighbours, chosen uniformly at random. We prove that throughout the low-temperature regime and at in-equilibrium time scales, 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. This demonstrates dynamical freezing in a spin glass system with logarithmically correlated energy levels.