Kac–Ward Formula and Its Extension to Order–Disorder Correlators Through a Graph Zeta Function

Michael Aizenman, Simone Warzel

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

A streamlined derivation of the Kac–Ward formula for the planar Ising model’s partition function is presented and applied in relating the kernel of the Kac–Ward matrices’ inverse with the correlation functions of the Ising model’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.

Original languageEnglish (US)
Pages (from-to)1755-1778
Number of pages24
JournalJournal of Statistical Physics
Volume173
Issue number6
DOIs
StatePublished - Dec 1 2018

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Ising model
  • Kac–Ward formula
  • Linear relations
  • Order–disorder correlation functions

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