%0 Journal Article
%A Eisenriegler, Erich
%T Critical behavior in rectangles with mixed boundaries
%J Physical review / E
%V 108
%N 4
%@ 2470-0045
%C Woodbury, NY
%I Inst.
%M FZJ-2023-04058
%P 044133
%D 2023
%X 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 f, 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 +f+f+ 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%$ 37978636
%U <Go to ISI:>//WOS:001095367500003
%R 10.1103/PhysRevE.108.044133
%U https://juser.fz-juelich.de/record/1017346