Description: Two-dimensional critical systems with mixed boundary conditions: Exact Ising results from conformal invariance and boundary-operator expansions

This title appears in the Scientific Report : 2021

Two-dimensional critical systems with mixed boundary conditions: Exact Ising results from conformal invariance and boundary-operator expansions

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 ene...

Personal Name(s):	Burkhardt, T. W.
	Eisenriegler, E. (Corresponding author)
Contributing Institute:	Theoretische Physik der Lebenden Materie; IBI-5
Published in:	Physical Review E Physical review / E, 103 103 (2021 2021) 1 1, S. 012120 012120
Imprint:	Woodbury, NY Inst. 2021 2021-01-19 2021-01-01
DOI:	10.1103/PhysRevE.103.012120
Document Type:	Journal Article
Research Program:	Molecular and Cellular Information Processing
Link:	OpenAccess
	Publikationsportal JuSER

Please use the identifier: http://hdl.handle.net/2128/27100 in citations.
Please use the identifier: http://dx.doi.org/10.1103/PhysRevE.103.012120 in citations.

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.