Diffusive dynamics of deposition-evaporation systems, jamming, and broken symmetries in related quantum-spin models

We investigate the dynamics of models involving deposition and evaporation of dimers, trimers, . . .k-mers, using analytical methods and numerical simulations. Autocorrelation functions show power-law decays in time, which are related to broken continuous symmetries in associated spin-1/2 Hamiltonians. These include the Heisenberg ferromagnet as the first nontrivial example. For k{≥}3 the models exhibit strongly nonergodic behavior. The numbers of both partially and fully jammed subspaces, within which the evolution takes place, increase exponentially with the size of the system. Evidence of finite-size scaling and universality over k is presented which supports a phenomenological diffusive picture for the dynamics in many subspaces.