@article{139f3357fcab42d9a158c6764b1b1070,
title = "Kac–Ward Formula and Its Extension to Order–Disorder Correlators Through a Graph Zeta Function",
abstract = "A streamlined derivation of the Kac–Ward formula for the planar Ising model{\textquoteright}s partition function is presented and applied in relating the kernel of the Kac–Ward matrices{\textquoteright} inverse with the correlation functions of the Ising model{\textquoteright}s order–disorder correlation functions. A shortcut for both is facilitated by the Bowen–Lanford graph zeta function relation. The Kac–Ward relation is also extended here to produce a family of non planar interactions on Z2 for which the partition function and the order–disorder correlators are solvable at special values of the coupling parameters/temperature.",
keywords = "Ising model, Kac–Ward formula, Linear relations, Order–disorder correlation functions",
author = "Michael Aizenman and Simone Warzel",
note = "Funding Information: This work was supported in part by the NSF grant DMS-1613296, the Weston Visiting Professorship at the Weizmann Institute (MA) and a PU Global Scholarship (SW). MA thanks the Faculty of Mathematics and Computer Sciences and the Faculty of Physics at WIS for the hospitality enjoyed there. We thank Hugo Duminil-Copin and Vincent Tassion for the pleasure of collaboration on topics related to this work. Copyright rests with the authors. Faithful reproduction of the article for non-commercial purpose is permitted. Funding Information: Acknowledgements This work was supported in part by the NSF grant DMS-1613296, the Weston Visiting Professorship at the Weizmann Institute (MA) and a PU Global Scholarship (SW). MA thanks the Faculty of Mathematics and Computer Sciences and the Faculty of Physics at WIS for the hospitality enjoyed there. We thank Hugo Duminil-Copin and Vincent Tassion for the pleasure of collaboration on topics related to this work. Publisher Copyright: {\textcopyright} 2018, The Author(s).",
year = "2018",
month = dec,
day = "1",
doi = "10.1007/s10955-018-2184-9",
language = "English (US)",
volume = "173",
pages = "1755--1778",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "6",
}