Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Annalen der Physik

Corner transfer matrix study of an inhomogeneous Ising model

Ingo Peschel, Roland Wunderling

Published Jan 1, 1992• 12 citations
Publisher

Abstract

Abstract We consider a planar Ising model with an extended defect described by couplings of the form K(r) = K·(1 + A/r). We determine the spectrum of the corner transfer matrix numerically and analytically and use it to calculate the local magnetization at the defect and the corresponding, non‐universal critical exponent.
DOI
10.1002/andp.19925040209

Related papers

Nonuniversal critical behaviour in planar Ising models with extended, radially symmetric defects

R. Z. Bariev, Ingo Peschel

Using conformal mapping and finite-size scaling the authors determine the local magnetic exponent near a defect characterized by couplings of the form J(r)=J(1+A/r). In accordance with phenomenological considerations, they find that it depends continuously on the amplitude A, both for a defect in the interior and on the boundary.

Journal of Physics A Mathematical and General•Jan 21, 1991•16 citations

Corner transfer matrices and corner magnetization for the Ising model

Brian Davies, Ingo Peschel

The authors consider the corner magnetization of an Ising square lattice with free edges along a diagonal direction. Using some remarkable properties of the corner transfer matrix, they give a unified treatment for various opening angles. The calculation of the magnetization is reduced to the solution of a matrix equation. In the thermodynamic limit they construct an explicit form of this equation and discuss its numerical and asymptotic solution and the results obtained thereby.

Journal of Physics A Mathematical and General•Mar 21, 1991•23 citations

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

T W Burhardt, Ferenc Iglói

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.

Journal of Physics A Mathematical and General•Jun 21, 1990•24 citations

Inhomogeneous critical Ising model

Ferenc Iglói

The spectrum of the transfer matrix of a semi-infinite two-dimensional Isin model with marginally inhomogeneous couplings has been determined exactly in the finite-size-scaling limit at the bulk critical point. Depending on the local temperature at the boundary the surface phase transition of this system is either of first order or of second order with nonuniversal critical exponents. For a second-order transition, the excitation energies of the transfer matrix are inversely proportional to the linear size (N) of the system, but the levels are not equidistantly spaced. On the other hand, for a first-order transition the lowest gap vanishes algegraically, but faster than 1/N.

Physical Review Letters•Jun 18, 1990•13 citations

Transfer matrix spectrum of two-dimensional layered Ising models

Laurent Frachebourg, Malte Henkel

A class of layered Ising models interpolating between the homogeneous Ising model and the McCoy-Wu model (1973) is studied. Critical exponents and the transfer matrix spectrum at the critical point are calculated numerically using finite-size scaling techniques and analytically by using an analogy with an electron gas in a crystal with impurities. The transfer matrix spectrum is compared with those of some strongly anisotropic critical systems.

Journal of Physics A Mathematical and General•Nov 7, 1991•3 citations

Application of Corner Transfer Matrix Renormalization Group Method to the Correlation Function of a Two-Dimensional Ising Model

He Chun-Shan, Zhibing Li

The correlation function of a two-dimensional Ising model is calculated by the corner transfer matrix renormalization group method. We obtain the critical exponent η = 0.2496 with few computer resources.

Chinese Physics Letters•Nov 1, 2003•0 citations
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.
The spectrum of the transfer matrix of a semi-infinite two-dimensional Isin model with marginally inhomogeneous couplings has been determined exactly in the finite-size-scaling limit at the bulk critical point. Depending on the local temperature at the boundary the surface phase transition of this system is either of first order or of second order with nonuniversal critical exponents. For a second-order transition, the excitation energies of the transfer matrix are inversely proportional to the linear size (N) of the system, but the levels are not equidistantly spaced. On the other hand, for a first-order transition the lowest gap vanishes algegraically, but faster than 1/N.