A thermodynamic system is ergodic when, given any (equilibrium) instance of the system, it eventually visits every other possible (equilibrium) state (of the same energy). One characteristic of spin glass systems is that, below the freezing temperature , instances are trapped in a "non-ergodic" set of states: the system may fluctuate between several states, but cannot transition to other states of equivalent energy. Intuitively, one can say that the system cannot escape from deep minima of the hierarchically disordered energy landscape; the distances between minima are given by an ultrametric, with tall energy barriers between minima. The participation ratio counts the number of states that are accessible from a given instance, that is, the number of states that participate in the ground state. The ergodic aspect of spin glass was instrumental in the awarding of half the 2021 Nobel Prize in Physics to Giorgio Parisi.
For physical systems, such as dilute manganese in copper, the freezing temperature is typically as low as 30 kelvins (−240 °C), and so the spin-glass magnetism appears to be practically without applications in daily life. The non-ergodic states and rugged energy landscapes are, however, quite useful in understanding the behavior of certain neural networks, including Hopfield networks, as well as many problems in computer science optimization and genetics.