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Cluster expansion for abstract polymer models. New bounds from an old approach
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We revisit the classical approach to cluster expansions, based on tree graphs, and establish a new convergence condition that improves those by Kotecky-Preiss and Dobrushin, as we show in some examples. The two ingredients of our approach are: (i) a careful consideration of the Penrose identity for truncated functions, and (ii) the use of iterated transformations to bound tree-graph expansions.
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A conditional no-go for resource-free magic-axis measurement on a static surface code
Under three stated assumptions, a resource-free static surface-code patch cannot sharply measure the magic axis at polynomial acceptance; it must pay with a resource, leave the dilute regime, or accept exponentially rarely.
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