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==== Simon-Lieb inequality ====
The Simon-Lieb inequality<ref>{{Cite journal |last=Simon |first=Barry |date=1980-10-01 |title=Correlation inequalities and the decay of correlations in ferromagnets |url=https://doi.org/10.1007/BF01982711 |journal=Communications in Mathematical Physics |language=en |volume=77 |issue=2 |pages=111–126 |doi=10.1007/BF01982711 |bibcode=1980CMaPh..77..111S |s2cid=17543488 |issn=1432-0916|url-access=subscription }}</ref> states that for any set <math>S</math> disconnecting <math>x</math> from <math>y</math> (e.g. the boundary of a box with <math>x</math> being inside the box and <math>y</math> being outside),
<math display="block">\langle \sigma_x \sigma_y \rangle \leq \sum_{z\in S} \langle \sigma_x \sigma_z \rangle \langle \sigma_z \sigma_y \rangle.</math>
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