Topological glass states

In connection with the recent discussion of topological order and topological phase transitions in quantum systems, we reexamine the circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local bonding enforces constraints on low-energy states that organize themselves into topologically distinct classes that break ergodicity but not any apparent symmetry as in the usual Landau theory of phase transitions. Various properties of such a topological glass are demonstrated using two classical Ising-like models.