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001017346 0247_ $$2doi$$a10.1103/PhysRevE.108.044133
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001017346 1001_ $$0P:(DE-Juel1)130628$$aEisenriegler, Erich$$b0$$eCorresponding author
001017346 245__ $$aCritical behavior in rectangles with mixed boundaries
001017346 260__ $$aWoodbury, NY$$bInst.$$c2023
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001017346 520__ $$aDensity 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.
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