Thus, for a system like an Ising spin glass with a rough ``energy landscape'' with many local minima, starting from a random initial configuration and running at a very low temperature T, the system will invariably get trapped in a local minimum, and never reach a thermalized state (at least not in the finite time of a real simulation).
This is analogous to quenching a metal, i.e., starting from a very hot (disordered) state, and rapidly cooling to a low temperature state (by plunging it into cold water, for example). For real metals, this will also produce a local minimum of the energy, leading to a brittle, non-crystalling state.