Critical Behavior in Rectangles with Mixed Boundaries
Abstract
Density profiles are investigated arising in a critical Ising model in two dimensions which is confined to a rectangular domain with uniform or mixed boundary conditions and arbitrary aspect ratio. For the cases in which the two vertical sides of the rectangle have up-spin boundary conditions + and the two horizontal sides with either down-spin boundary conditions or with free-spin boundary conditions , exact results are presented for the density profiles of the energy and the order parameter which display a surprisingly rich behavior. The new results follow by means of conformal transformations from known results in the half plane with and boundary conditions. The corners with mixed boundary conditions lead to interesting behavior, even in the limit of a half-infinite strip. The behavior near these corners can be described by a ``Corner-Operator-Expansion'', which is discussed in the second part of the paper. The analytic predictions agree very well with simulations, with no adjustable parameters.
Cite
@article{arxiv.2307.07831,
title = {Critical Behavior in Rectangles with Mixed Boundaries},
author = {E. Eisenriegler},
journal= {arXiv preprint arXiv:2307.07831},
year = {2023}
}