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• W3047889439 abstract "With conformal-invariance methods, Burkhardt, Guim, and Xue studied the critical Ising model, defined on the upper half plane $y>0$ with different boundary conditions $a$ and $b$ on the negative and positive $x$ axes. For $ab=-+$ and $f+$, they determined the one and two-point averages of the spin $sigma$ and energy $epsilon$. Here $+$, $-$, and $f$ stand for spin-up, spin-down, and free-spin boundaries, respectively. The case $+-+-+dots$, where the boundary conditions switch between $+$ and $-$ at arbitrary points, $zeta_1$, $zeta_2$, $dots$ on the $x$ axis was also analyzed. In this paper the alternating boundary conditions $+f+f+dots$ and the case $-f+$ of three different boundary conditions are considered. Exact results for the one and two-point averages of $sigma$, $epsilon$, and the stress tensor $T$ are derived. Using the results for $langle Trangle$, the critical Casimir interaction with the boundary of a wedge-shaped inclusion is analyzed for mixed boundary conditions. The paper also includes a comprehensive discussion of boundary-operator expansions in two-dimensional critical systems with mixed boundary conditions. Two types of expansions - away from switching points of the boundary condition and at switching points - are considered. The asymptotic behavior of two-point averages is expressed in terms of one-point averages with the help of the expansions. We also consider the strip geometry with mixed boundary conditions and derive the distant-wall corrections to one-point averages near one edge due to the other edge using the boundary-operator expansions. The predictions of the boundary-operator expansions are consistent with exact results for Ising systems." @default.
• W3047889439 created "2020-08-13" @default.
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• W3047889439 date "2021-01-19" @default.
• W3047889439 modified "2023-10-16" @default.
• W3047889439 title "Two-dimensional critical systems with mixed boundary conditions: Exact Ising results from conformal invariance and boundary-operator expansions" @default.
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• W3047889439 doi "https://doi.org/10.1103/physreve.103.012120" @default.
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• W3047889439 hasPublicationYear "2021" @default.
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