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

Physica A Statistical Mechanics and its Applications

Layering transitions in Ising model thin films. A real space renormalization group analysis

A. Benyoussef, Hamid Ez-zahraouy A

Published May 1, 1994• 25 citations
Publisher
DOI
10.1016/0378-4371(94)90125-2

Related papers

Real space renormalization group calculations for the 3-dimensional Ising model

J. Oitmaa, Michael N. Barber

Physica B+C•Jan 1, 1977•4 citations

Real space renormalization group study of the random bond Ising model

Moshe Schwartz, Shmuel Fishman

Physica A Statistical Mechanics and its Applications•Nov 1, 1980•12 citations

Real space renormalization group study of the two-dimensional super-antiferromagnetic Ising model

Isabel Cristina Souza Dinóla, A. Saguia, B. Boechat

Physics Letters A•Mar 15, 2009•4 citations

Application of the real space dynamic renormalization group method to the one-dimensional kinetic ising model

Gene F. Mazenko, James H. Luscombe

Annals of Physics•Mar 1, 1981•11 citations

Application of the real space dynamic renormalization group method to the one-dimensional kinetic Ising model

James Franck Institute

Annals of Physics•Feb 1, 1981•0 citations

Is the hyperscaling relation violated below the upper critical dimension in some particular cases?

H. T. Diep, Van Thanh Ngo

In this review, we show our results with new interpretation on the critical exponents of thin films obtained by high-performance multi-histogram Monte Carlo simulations. The film thickness $N_z$ consists of a few layers up to a dozen of layers in the $z$ direction. The free boundary condition is applied in this direction while in the $xy$ plane periodic boundary conditions are used. Large $xy$ plane sizes are used for finite-size scaling. The Ising model is studied with nearest-neighbor (NN) interaction. When $N_z=1$, namely the two-dimensional (2D) system, we find the critical exponents given by the renormalization group. While, for $N_z>1$, the critical exponents calculated with the high-precision multi-histogram technique show that they deviate slightly but systematically from the 2D values. If we use these values of critical exponents in the hyperscaling relation with $d=2$, then the hyperscaling relation is violated. However, if we use the hyperscaling relation and the critical exponents obtained for $N_z>1$ to calculate the dimension of the system, we find the system dimension slightly larger than 2. This can be viewed as an "effective" dimension. More discussion is given in the paper. We also show the cross-over between the first- and second-order transition while varying the film thickness in an antiferromagnetic FCC Ising frustrated thin film. In addition, we will show evidence that when a 2D system has two order parameters of different symmetries with a single transition, the critical exponents are new, suggesting a universality class of coupled two-symmetry breakings. In this case, the 2D hyperscaling does not hold. Another case is the 3D Ising model coupled to the lattice vibration: the critical exponents deviate from the 3D Ising ones, the results suggest the violation of the hyperscaling.

arXiv:2507.02159•Jul 2, 2025•0 citations
In this review, we show our results with new interpretation on the critical exponents of thin films obtained by high-performance multi-histogram Monte Carlo simulations. The film thickness NzN_zNz​ consists of a few layers up to a dozen of layers in the zzz direction. The free boundary condition is applied in this direction while in the xyxyxy plane periodic boundary conditions are used. Large xyxyxy plane sizes are used for finite-size scaling. The Ising model is studied with nearest-neighbor (NN) interaction. When Nz=1N_z=1Nz​=1, namely the two-dimensional (2D) system, we find the critical exponents given by the renormalization group. While, for Nz>1N_z>1Nz​>1, the critical exponents calculated with the high-precision multi-histogram technique show that they deviate slightly but systematically from the 2D values. If we use these values of critical exponents in the hyperscaling relation with d=2d=2d=2, then the hyperscaling relation is violated. However, if we use the hyperscaling relation and the critical exponents obtained for Nz>1N_z>1Nz​>1 to calculate the dimension of the system, we find the system dimension slightly larger than 2. This can be viewed as an "effective" dimension. More discussion is given in the paper. We also show the cross-over between the first- and second-order transition while varying the film thickness in an antiferromagnetic FCC Ising frustrated thin film. In addition, we will show evidence that when a 2D system has two order parameters of different symmetries with a single transition, the critical exponents are new, suggesting a universality class of coupled two-symmetry breakings. In this case, the 2D hyperscaling does not hold. Another case is the 3D Ising model coupled to the lattice vibration: the critical exponents deviate from the 3D Ising ones, the results suggest the violation of the hyperscaling.