Journal Article

FZJ-2021-00909

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Two-dimensional critical systems with mixed boundary conditions: Exact Ising results from conformal invariance and boundary-operator expansions

Burkhardt, T. W. ; Eisenriegler, E. (Corresponding author)FZJ*

2021
Inst. Woodbury, NY

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Please use a persistent id in citations: http://hdl.handle.net/2128/27100  doi:10.1103/PhysRevE.103.012120

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 σ and energy ε. Here +,−, and f stand for spin-up, spin-down, and free-spin boundaries, respectively. The case +−+−+⋯, where the boundary condition switches between + and − at arbitrary points, ζ1,ζ2,⋯ on the x axis was also analyzed. In the first half of this paper a similar study is carried out for the alternating boundary condition +f+f+⋯ and the case −f+ of three different boundary conditions. Exact results for the one- and two-point averages of σ,ε, and the stress tensor T are derived with conformal-invariance methods. From the results for ⟨T⟩, the critical Casimir interaction with the boundary of a wedge-shaped inclusion is derived for mixed boundary conditions. In the second half of the paper, arbitrary two-dimensional critical systems with mixed boundary conditions are analyzed with boundary-operator expansions. Two distinct types of expansions—away from switching points of the boundary condition and at switching points—are considered. Using the expansions, we express the asymptotic behavior of two-point averages near boundaries in terms of one-point averages. 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. Finally we confirm the consistency of the predictions obtained with conformal-invariance methods and with boundary-operator expansions, in the the first and second halves of the paper.

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Contributing Institute(s):

1. Theoretische Physik der Lebenden Materie (IBI-5)

Research Program(s):

1. 524 - Molecular and Cellular Information Processing (POF4-524) (POF4-524)

Appears in the scientific report 2021

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Electronics and Telecommunications Collection ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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