We present a large-scale simulation of the three-dimensional and mean-field spin glasses down to a very low but finite temperature. We extrapolate pertinent observables, e.g., the disorder-averaged central weight to zero temperature, finding that many thermodynamic states at a finite temperature and two ground states at zero temperature are fully compatible. While the disorder-averaged central weight monotonically decreases with decreasing temperature, this is far from true for individual samples. This motivates us to link this behavior with the well-known temperature chaos. At an observing temperature, a sample may or may not have pure state coexistence depending on whether it is undergoing temperature chaos, which is a random process. Therefore, temperature chaos is likely responsible for the emergence of many pure states, providing a natural and intuitive explanation for the coexistence of expensive domain-wall excitations and many pure states at the disorder-averaged level.

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• Classical statistical mechanics
• Disordered systems
• Spin glasses
• Monte Carlo methods