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 -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