TY - JOUR AU - Eisenriegler, Erich TI - Critical behavior in rectangles with mixed boundaries JO - Physical review / E VL - 108 IS - 4 SN - 2470-0045 CY - Woodbury, NY PB - Inst. M1 - FZJ-2023-04058 SP - 044133 PY - 2023 AB - 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. LB - PUB:(DE-HGF)16 C6 - 37978636 UR - <Go to ISI:>//WOS:001095367500003 DO - DOI:10.1103/PhysRevE.108.044133 UR - https://juser.fz-juelich.de/record/1017346 ER -