  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.
