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

Phase diagram of the 2d Ashkin-Teller model: numerical transfer-matrix approach

G. Kamieniarz, Piotr Kozłowski, Raf Dekeyser

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

The aim of this work is to determine as accurately as possible the phase diagram of the Askhin-Teller model (AT) in two dimensions. Calculations for the simple square L x L lattice using transfer matrix techniques were performed (L= 2,...,9) to find the ratio QL. Exploiting finite-size scaling for QL, all unknown critical lines were obtained with good accuracy.

Related papers

Improved Phase Diagrams of Ashkin-Teller Model

P. Pawlicki, G. Kamieniarz, Piotr Kozłowski +2 more

The phase diagram of the Askhii-Teller model in two dimensions is determined.Numerical calculations are performed for the simple square L x L lattice using transfer matrix technique.Exploiting finite-size scaling all unknown critical lines were obtained with good accuracy.An extended version of the Áskkin-Teller model is also considered within the molecular field renormalization group method and the critical surface for three-parameter odd-parity Hamiltonian is calculated.

Acta Physica Polonica A•Aug 1, 1997•1 citation

Critical Ising lines of the d=2 Ashkin-Teller model

G. Kamieniarz, Piotr Kozłowski, Raf Dekeyser

The universal critical point ratio Q is exploited to determine positions of the critical Ising transition lines on the phase diagram of the Ashkin-Teller model on the square lattice. A leading-order expansion of the ratio Q in the presence of a nonvanishing thermal field is found from finite-size scaling and the corresponding expression is fitted by the accurate perturbative transfer-matrix data calculations for the L\ifmmode\times\else\texttimes\fi{}L square clusters with L\ensuremath{\leqslant}9.

arXiv:cond-mat/9803277•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Mar 1, 1997•19 citations

Numerical study of the spin-1 Ashkin-Teller model

M. Badehdah, Smain Bekhechi, A. Benyoussef +1 more

Two nonperturbative methods by means of the transfer-matrix finite-size-scaling and Monte Carlo simulations are used to investigate the spin-1 Ashkin-Teller model (ATM). We have obtained rich phase diagrams with first- and second-order phase transitions with several multicritical points of higher order. Also this model exhibits a partially ordered phase ${\mathrm{PO}}_{2}$ which does not exist in the spin-1/2 Ashkin-Teller model (ATM). Finally, the critical behavior of this model is discussed.

Physical review. B, Condensed matter•Mar 1, 1999•15 citations

Phase diagram and critical properties of the (1+1)-dimensional Ashkin-Teller model

Ferenc Iglói, Jenő Sólyom

The (1+1)-dimensional Ashkin-Teller model is studied by the renormalisation group method and by the finite lattice extrapolation technique. The possible phases and their boundaries in an extended space of couplings are determined from the degeneracy structure of the low-lying levels in the thermodynamic limit. The critical behaviour is investigated for ferromagnetic couplings using increasing block sizes in the renormalisation transformation. The line of fixed points and its bifurcation at the Potts fixed point is studied.

Journal of Physics A Mathematical and General•May 11, 1984•22 citations

Monte Carlo simulations of Ising-like phase transitions in the three-dimensional Ashkin-Teller model

Grzegorz Musiał, L. Dębski, G. Kamieniarz

The results of the large-scale Monte Carlo simulations of the continuous phase transitions in the three-dimensional Ashkin-Teller model on a cubic lattice are presented in the two-parameter space. The invariance of the ratio of the square of the second moment of the order parameter to its fourth moment in the critical region and the Metropolis algorithm are exploited. Using the universality hypothesis and the finite-size-scaling analysis, the accurate positions of the continuous phase-transition lines are calculated and their Ising character is confirmed. Approximate locations of the tricritical points are also estimated.

Physical review. B, Condensed matter•Jun 28, 2002•27 citations

The critical point ratio for some d = 2 classical models

Gregory Kamieniarz, Piotr Kozłowski, Raf Dekeyser

The universal critical point ratio of the square of the second moment of the order parameter to its fourth moment, denoted as Q, is exploited to determine the position of the critical Ising transition lines in the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the Q ratio in the presence of a non-vanishing thermal field is found from finite-size scaling and the corresponding expression is fitted to the accurate perturbative transfer-matrix data for the L x L squaxe clusters with L <= 9. The same method is used to determine the critical Ising transition line on the phase diagram of the Blume-Capel (BC) model (L <= 11). We have also calculated the Q ratio for the q=3 Potts model in the critical point. The previously predicted scaling relation for this universality class is confirmed by our results for L <= 12.

•Jan 1, 1996•0 citations
The aim of this work is to determine as accurately as possible the phase diagram of the Askhin-Teller model (AT) in two dimensions. Calculations for the simple square L x L lattice using transfer matrix techniques were performed (L= 2,...,9) to find the ratio QL. Exploiting finite-size scaling for QL, all unknown critical lines were obtained with good accuracy.
The universal critical point ratio Q is exploited to determine positions of the critical Ising transition lines on the phase diagram of the Ashkin-Teller model on the square lattice. A leading-order expansion of the ratio Q in the presence of a nonvanishing thermal field is found from finite-size scaling and the corresponding expression is fitted by the accurate perturbative transfer-matrix data calculations for the L\ifmmode\times\else\texttimes\fi{}L square clusters with L\ensuremath{\leqslant}9.
Two nonperturbative methods by means of the transfer-matrix finite-size-scaling and Monte Carlo simulations are used to investigate the spin-1 Ashkin-Teller model (ATM). We have obtained rich phase diagrams with first- and second-order phase transitions with several multicritical points of higher order. Also this model exhibits a partially ordered phase PO2{\mathrm{PO}}_{2}PO2​ which does not exist in the spin-1/2 Ashkin-Teller model (ATM). Finally, the critical behavior of this model is discussed.
The (1+1)-dimensional Ashkin-Teller model is studied by the renormalisation group method and by the finite lattice extrapolation technique. The possible phases and their boundaries in an extended space of couplings are determined from the degeneracy structure of the low-lying levels in the thermodynamic limit. The critical behaviour is investigated for ferromagnetic couplings using increasing block sizes in the renormalisation transformation. The line of fixed points and its bifurcation at the Potts fixed point is studied.
The results of the large-scale Monte Carlo simulations of the continuous phase transitions in the three-dimensional Ashkin-Teller model on a cubic lattice are presented in the two-parameter space. The invariance of the ratio of the square of the second moment of the order parameter to its fourth moment in the critical region and the Metropolis algorithm are exploited. Using the universality hypothesis and the finite-size-scaling analysis, the accurate positions of the continuous phase-transition lines are calculated and their Ising character is confirmed. Approximate locations of the tricritical points are also estimated.
The universal critical point ratio of the square of the second moment of the order parameter to its fourth moment, denoted as Q, is exploited to determine the position of the critical Ising transition lines in the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the Q ratio in the presence of a non-vanishing thermal field is found from finite-size scaling and the corresponding expression is fitted to the accurate perturbative transfer-matrix data for the L x L squaxe clusters with L <= 9. The same method is used to determine the critical Ising transition line on the phase diagram of the Blume-Capel (BC) model (L <= 11). We have also calculated the Q ratio for the q=3 Potts model in the critical point. The previously predicted scaling relation for this universality class is confirmed by our results for L <= 12.