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

Journal of Physics A Mathematical and General

Corner transfer matrices and corner magnetization for the Ising model

Brian Davies, Ingo Peschel

Published Mar 21, 1991• 23 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/24/6/021

Related papers

A unified treatment of Ising model magnetizations

Brian Davies, Ingo Peschel

Abstract We show how the spontaneous bulk, surface and corner magnetizations in the square lattice Ising model can all be obtained within one approach. The method is based on functional equations which follow from the properties of corner transfer matrices and vertex operators and which can be derived graphically. In all cases, exact analytical expressions for general anisotropy are obtained. Known results, including several for which only numerical computation was previously possible, are verified and new results related to general anisotropy and corner angles are obtained.

arXiv:cond-mat/9610212•Annalen der Physik•Jan 1, 1997•10 citations

A unified treatment of Ising model magnetizations

Brian Davies, Ingo Peschel, Fachbereich Physik +1 more

Abstract We show how the spontaneous bulk, surface and corner magnetizations in the square lattice Ising model can all be obtained within one approach. The method is based on functional equations which follow from the properties of corner transfer matrices and vertex operators and which can be derived graphically. In all cases, exact analytical expressions for general anisotropy are obtained. Known results, including several for which only numerical computation was previously possible, are verified and new results related to general anisotropy and corner angles are obtained.

•Aug 17, 2016•8 citations

Variational approach to the scaling function of the 2D Ising model in a magnetic field

Vladimir V. Mangazeev, Murray T. Batchelor, Vladimir V. Bazhanov +1 more

The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data are in perfect agreement with the remarkable field theory results obtained by Fonseca and Zamolodchikov, as well as with many previously known exact and numerical results for the 2D Ising model. This includes excellent agreement with analytic results for the magnetic susceptibility obtained by Orrick, Nickel, Guttmann and Perk. In general, the high precision of the numerical results underlines the potential and full power of the variational corner transfer matrix approach.

arXiv:0811.3271•Journal of Physics A Mathematical and Theoretical•Dec 19, 2008•15 citations

Corner transfer matrix study of an inhomogeneous Ising model

Ingo Peschel, Roland Wunderling

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.

Annalen der Physik•Jan 1, 1992•12 citations

Exact Solutions of the Ising Model

Ludwig Ridderstolpe

This report presents the general Ising model and its basic assumptions. This study aims to, from diagonalization of the Transfer Matrix, obtain the Helmholtz free energy and the exclusion of a phase transition for the one-dimensional Ising model under an external magnetic field. Furthermore from establishing the commutation relations of the Transfer matrices and using the Kramers-Wannier duality one finds the free energy and the presence of a phase transition for the square-lattice Ising model.

•Jan 1, 2017•0 citations

Finite-size scaling of corner transfer matrices for the two-dimensional Ising model

Ingo Peschel

The eigenvalue spectra of generalised corner transfer matrices are calculated for an Ising model on a square lattice. The predictions of conformal invariance at the critical point are thereby verified.

Journal of Physics A Mathematical and General•Feb 7, 1988•9 citations
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.
Abstract We show how the spontaneous bulk, surface and corner magnetizations in the square lattice Ising model can all be obtained within one approach. The method is based on functional equations which follow from the properties of corner transfer matrices and vertex operators and which can be derived graphically. In all cases, exact analytical expressions for general anisotropy are obtained. Known results, including several for which only numerical computation was previously possible, are verified and new results related to general anisotropy and corner angles are obtained.
Abstract We show how the spontaneous bulk, surface and corner magnetizations in the square lattice Ising model can all be obtained within one approach. The method is based on functional equations which follow from the properties of corner transfer matrices and vertex operators and which can be derived graphically. In all cases, exact analytical expressions for general anisotropy are obtained. Known results, including several for which only numerical computation was previously possible, are verified and new results related to general anisotropy and corner angles are obtained.
The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data are in perfect agreement with the remarkable field theory results obtained by Fonseca and Zamolodchikov, as well as with many previously known exact and numerical results for the 2D Ising model. This includes excellent agreement with analytic results for the magnetic susceptibility obtained by Orrick, Nickel, Guttmann and Perk. In general, the high precision of the numerical results underlines the potential and full power of the variational corner transfer matrix approach.