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If you look at the paper by Hastings and Koma, https://arxiv.org/abs/math-ph/0507008, they claim to prove the following: When two observables commute with each other at large distance, the connected correlation function decays exponentially under the gap assumption. The key word here is "connected." For the $Z_i$'s (which trivially commute with ...

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Putting aside whether such an early Universe has hadrons, which would still be massive: if all particles travel at the speed of light, then none of them would experience the flow of time, so in such a universe is it still possible to assign an observing reference frame which does experience the flow of time? Special relativity would still have reference ...

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The theorem is quite robust to variations in the interaction - it only requires that it does not violate local continuity. The biggest physical limitation is that one needs A LOT of infra-red fluctuations to destabilize the ordered state, which are cut off by the size of the sample in any real setting. In 2D, the effect of the theorem is only logarithmic in ...

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