Diffusing Reconstituting Dimers: a Simple Model of Broken Ergodicity and Ageing

We consider a model of assisted diffusion of hard-core particles on a line. In this model, a particle can jump left or right by two steps to an unoccupied site, but only if the the site in between is occupied. We show that this model is strongly non-ergodic, and the phase space breaks up into mutually disconnected sectors. The number of such sectors increases as the exponential of the size of the system. Within a sector, the model can be shown to be equivalent to the Heisenberg model, and is exactly soluble. We study how time-dependent autocorrelation functions in the model depend on the sector. We also show how this strong breaking of ergodicity ( which can be thought of as an infinity of conservation laws) affects the hydrodynamical description of the long wavelength density fluctuations in the system. Finally, we study the effect of allowing transitions between sectors at a very slow rate.