English

A formula for boundary correlations of the critical Ising model

Mathematical Physics 2021-08-17 v3 Combinatorics math.MP Probability

Abstract

Given a finite rhombus tiling of a polygonal region in the plane, the associated critical ZZ-invariant Ising model is invariant under star-triangle transformations. We give a simple matrix formula describing spin correlations between boundary vertices in terms of the shape of the region. When the region is a regular polygon, our formula becomes an explicit trigonometric sum.

Keywords

Cite

@article{arxiv.2010.13345,
  title  = {A formula for boundary correlations of the critical Ising model},
  author = {Pavel Galashin},
  journal= {arXiv preprint arXiv:2010.13345},
  year   = {2021}
}

Comments

21 pages, 5 figures; v2: Bibliography updates, section structure reorganized; v3: Final version to appear in Probab. Theory Related Fields