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

arXiv:cond-mat/0101201 · Journal of Physics A Mathematical and General

Critical exponents of the two-layer Ising model

Zhibing Li, Zhigang Shuai, Q Wang, H. J. Luo, Lothar Schülke

Published Jul 27, 2001• 35 citations
arXivHTMLPDF

Abstract

The symmetric two-layer Ising model (TLIM) is studied by the corner transfer matrix renormalization group method. The critical points and critical exponents are calculated. It is found that the TLIM belongs to the same universality class as the Ising model. The shift exponent is calculated to be 1.773, which is consistent with the theoretical prediction of 1.75 with 1.3% deviation.

DOI
10.1088/0305-4470/34/31/302

Related papers

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

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

何春山, 李志兵

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

Chinese Physics Letters•Jan 1, 2003•0 citations

Critical Point of a Symmetric Vertex Model

Kouji Ueda, 両太 大谷, Yukinobu Nishio +2 more

We study a symmetric vertex model, that allows 10 vertex configurations, by use of the corner transfer matrix renormalization group (CTMRG), a variant of DMRG. The model has a critical point that belongs to the Ising universality class.

arXiv:cond-mat/0501277•Journal of the Physical Society of Japan•Jun 1, 2005•6 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

Calculation of the shift exponent for the two-layer three-state Potts model using the transfer matrix method

Kamran Mardani, Behrouz Mirza, Mehrdad Ghaemi

A finite-size scaling approach based on the transfer matrix method is developed to calculate the critical temperature and critical exponent of the symmetric and the asymmetric two-layer three-state Potts models. For similar intralayer interactions our calculation of the shift exponent $\ensuremath{\varphi}$ confirm some scaling arguments which predict $\ensuremath{\varphi}=\ensuremath{\gamma}$, where $\ensuremath{\gamma}$ is the susceptibility exponent. For unequal intralayer interactions we have obtained $\ensuremath{\varphi}=0.5$ which differ from the prediction $\ensuremath{\varphi}=\ensuremath{\gamma}∕2$ of a generalized mean-field theory.

arXiv:cond-mat/0510011•Physical Review E•Aug 24, 2005•6 citations

Tensor renormalization-group study of the surface critical behavior of a frustrated two-layer Ising model

Christophe Chatelain

Abstract Two replicas of a 2D Ising model are coupled by frustrated spin-spin interactions. It is known that this inter-layer coupling is marginal and that the bulk critical behavior belongs to the Ashkin–Teller (AT) universality class, as the J 1 − J 2 Ising model. In this work, the surface critical behavior is studied numerically by tensor renormalization-group calculations. The bond-weight tensor renormalization group algorithm is extended to tackle systems with boundaries. It is observed that the two-fold degeneracy of the surface magnetic scaling dimension of the AT model is lifted in the frustrated two-layer Ising model (F2LIM). The splitting is explained by the breaking of the Z 2 -symmetry under spin reversal of a single Ising replica in the F2LIM. The two distinct surface magnetic scaling dimensions x 1 s and x 2 s of the F2LIM satisfies a simple duality relation x 1 s = 1 / 4 x 2 s .

arXiv:2510.21269•Journal of Statistical Mechanics Theory and Experiment•Feb 1, 2026•0 citations
The symmetric two-layer Ising model (TLIM) is studied by the corner transfer matrix renormalization group method. The critical points and critical exponents are calculated. It is found that the TLIM belongs to the same universality class as the Ising model. The shift exponent is calculated to be 1.773, which is consistent with the theoretical prediction of 1.75 with 1.3% deviation.
A finite-size scaling approach based on the transfer matrix method is developed to calculate the critical temperature and critical exponent of the symmetric and the asymmetric two-layer three-state Potts models. For similar intralayer interactions our calculation of the shift exponent $\ensuremath{\varphi}$ confirm some scaling arguments which predict $\ensuremath{\varphi}=\ensuremath{\gamma}$, where $\ensuremath{\gamma}$ is the susceptibility exponent. For unequal intralayer interactions we have obtained $\ensuremath{\varphi}=0.5$ which differ from the prediction $\ensuremath{\varphi}=\ensuremath{\gamma}∕2$ of a generalized mean-field theory.
Abstract Two replicas of a 2D Ising model are coupled by frustrated spin-spin interactions. It is known that this inter-layer coupling is marginal and that the bulk critical behavior belongs to the Ashkin–Teller (AT) universality class, as the J 1 − J 2 Ising model. In this work, the surface critical behavior is studied numerically by tensor renormalization-group calculations. The bond-weight tensor renormalization group algorithm is extended to tackle systems with boundaries. It is observed that the two-fold degeneracy of the surface magnetic scaling dimension of the AT model is lifted in the frustrated two-layer Ising model (F2LIM). The splitting is explained by the breaking of the Z 2 -symmetry under spin reversal of a single Ising replica in the F2LIM. The two distinct surface magnetic scaling dimensions x 1 s and x 2 s of the F2LIM satisfies a simple duality relation x 1 s = 1 / 4 x 2 s .