Transient subdiffusion from an Ising environment

TL;DR

This paper models a particle performing a CTRW in an Ising environment, revealing transient subdiffusion at criticality and ergodicity breaking, with the duration of anomalous diffusion depending on environmental scale and temperature proximity to criticality.

Contribution

It introduces a coupled CTRW-Ising model showing how environmental criticality induces transient subdiffusion and ergodicity breaking, highlighting the role of finite size and temperature.

Findings

Subdiffusion occurs at the Ising critical temperature.

Finite environment size causes subdiffusion to be transient.

Ergodicity breaking appears at intermediate times and depends on system parameters.

Abstract

We introduce a model, in which a particle performs a continuous time random walk (CTRW) coupled to an environment with Ising dynamics. The particle shows locally varying diffusivity determined by the geometrical properties of the underlying Ising environment, that is, the diffusivity depends on the size of the connected area of spins pointing in the same direction. The model shows anomalous diffusion when the Ising environment is at critical temperature. We show that any finite scale introduced by a temperature different from the critical one, or a finite size of the environment, cause subdiffusion only during a transient time. The characteristic time, at which the system returns to normal diffusion after the subdiffusive plateau depends on the limiting scale and on how close the temperature is to criticality. The system also displays apparent ergodicity breaking at intermediate time, while ergodicity breaking at longer time occurs only under the idealized infinite environment at the critical temperature.