A note on the high-fugacity hard-core model on bounded-degree bipartite expander graphs
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Jenssen, Keevash and Perkins give an FPTAS and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs. Their method is based on Pirogov-Sinai theory -- using cluster expansion to obtain a zero-free region for a so-called polymer partition function in the complex plane, and then approximating the polymer partition function using methods of Barvinok and Patel and Regts. In this note, we circumvent the zero-free analysis and the generalisation to complex fugacities, showing that the polymer partition function can be approximated using Glauber dynamics. The proof that Glauber dynamics mixes rapidly is easy and is based on using the sizes of the disagreeing polymers as a distance function.
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