Zero-temperature 2D stochastic Ising model and anisotropic curve-shortening flow

Zero-Temperature Stochastic Ising Model

We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of +1 or −1 to each site in Z, is the zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with Glauber dynamics): the initial state is chosen uniformly at random and then each site, at rate one, p...

Information Storage in the Stochastic Ising Model at Zero Temperature

Most information systems store data by modifying the local state of matter, in the hope that atomic (or subatomic) local interactions would stabilize the state for a sufficiently long time, thereby allowing later recovery. In this work we initiate the study of information retention in locally-interacting systems. The evolution in time of the interacting particles is modeled via the stochastic I...

Ergodicity of Stochastic Curve Shortening Flow in the Plane

We study models of the motion by mean curvature of an (1+1) dimensional interface with random forcing. For the well-posedness of the models we prove existence and uniqueness for certain degenerate nonlinear stochastic evolution equations in the variational framework of Krylov-Rozovskĭı, replacing the standard coercivity assumption by a Lyapunov type condition. Ergodicity is established for the ...

Stretched Exponential Fixation in Stochastic Ising Models at Zero Temperature

Zero-temperature freezing in the three-dimensional kinetic Ising model.

We investigate the relaxation of the Ising-Glauber model on a periodic cubic lattice after a quench to zero temperature. In contrast to the conventional picture from phase-ordering kinetics, we find the following: (i) domains at long time are highly interpenetrating and topologically complex, with average genus growing algebraically with system size; (ii) the long-time state is almost never sta...