Semi-infinite two-dimensional Ising model with marginally inhomogeneous couplings and conformal invariance

T. W. Burhardt, F. Iglói

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

The authors consider a semi-infinite two-dimensional Ising model with nearest-neighbour couplings that deviate from the bulk critical couplings by Al-2, where l is the distance from the surface. The surface critical exponents of this system are non-universal. Under a conformal mapping onto a strip of width L, the Al-1 inhomogeneity transforms into A((L/ pi )sin( pi L/L))-1. For the square lattice the spectrum of the transfer matrix in the strip geometry is calculated exactly in the extreme anisotropic limit. The analytical results and numerical results for the triangular lattice are compared with predictions of conformal invariance.

Original languageEnglish
Article number009
JournalJournal of Physics A: Mathematical and General
Volume23
Issue number12
DOIs
Publication statusPublished - 1990

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Conformal Invariance
Ising model
Invariance
Pi
Ising Model
Strip
invariance
strip
Conformal mapping
Surjection
conformal mapping
Triangular Lattice
Conformal Mapping
Transfer Matrix
Square Lattice
Inhomogeneity
Critical Exponents
Nearest Neighbor
inhomogeneity
Extremes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

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AB - The authors consider a semi-infinite two-dimensional Ising model with nearest-neighbour couplings that deviate from the bulk critical couplings by Al-2, where l is the distance from the surface. The surface critical exponents of this system are non-universal. Under a conformal mapping onto a strip of width L, the Al-1 inhomogeneity transforms into A((L/ pi )sin( pi L/L))-1. For the square lattice the spectrum of the transfer matrix in the strip geometry is calculated exactly in the extreme anisotropic limit. The analytical results and numerical results for the triangular lattice are compared with predictions of conformal invariance.

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