Glassy behaviour in a 3-state spin model

In this paper we study a simple spin model which has a non-interacting Hamiltonian but constrained dynamics. The model, which is a simplification of a purely topological cellular model (Davison L and Sherrington D 2000 J. Phys. A: Math. Gen. 338615, Aste T and Sherrington D 1999 J. Phys. A: Math. Gen. 32 7049), displays glassy behaviour, involves activated processes and exhibits two-step relaxation. This is a consequence of the existence of annihilation-diffusion processes on two distinct timescales, one temperature independent and the other an exponential function of inverse temperature. In fact, there are several such inter-coupled microscopic processes and great richness therein. Two versions of the model are considered, one with a single absorbing ground state and the other with a highly degenerate ground state. These display qualitatively similar but quantitatively distinct macroscopic behaviour and related, but different, microscopic behaviour. © 2001 IOP Publishing Ltd