Ergodicity Breaking
Ergodicity is the assumption that a system, at a given temperature, explores the full phase space, just each state takes different probabilities. In an Ising ferromagnet below this does not happen. If, never mind how close they are, the system has chosen a global magnetization, and the phase space is divided into two regions. From one of them it is impossible to reach the other, unless a magnetic field is applied, or temperature is raised above .
See also superselection sector
Read more about this topic: Critical Phenomena
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