Reproduce “On Zeros and Algorithms for Disordered Systems II: The Antiferromagnetic Ising Model up to Kesten-Stigum” on OpenResearch
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About this paper
Ferenc Bencs, Brice Huang, Daniel Z. Lee, Kuikui Liu, Guus Regts
The authors give a deterministic algorithm to approximate the antiferromagnetic Ising partition function on uniformly random d-regular graphs. For fixed d≥3 and gap δ>0, it uses a complex-temperature zero-free region and analytic interpolation, running in (n/ε)^C(d,δ) time. At β≤(1−δ)βKS(d), it achieves multiplicative e±ε accuracy with probability 1−o_n(1) over the graph; the guarantee stops short of the threshold.
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