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 the Physical Society of Japan

Determination of the Critical Points of Antiferromagnetic Ising Model with Next Nearest Neighbour Interactions on the Triangular Lattice

Seiji Miyashita, Hidetsugu Kitatani, Yasumasa Kanada

Published May 15, 1991• 25 citations
Publisher

Abstract

Positions of critical temperatures of antiferromagnetic Ising model with ferromagnetic next nearest neighbour interactions on the triangular lattice are investigated by making use of their properties of the Kosterlitz-Thouless type of phase transition. In particular, finite-size scaling method and Monte Carlo Renormalization Group methods (MCRG) with flow diagrams of the anomalous dimension η show the fixed line structure where the correlation length diverges. Another MCRG with flow diagram of the stiffness constant also shows a critical property clearly. The temperature dependence of the long range order is also discussed in order to locate the lower critical point.

DOI
10.1143/jpsj.60.1523

Related papers

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

М. К. Бадиев, Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.

Journal of Experimental and Theoretical Physics•Oct 1, 2016•9 citations

Monte Carlo Study of a Triangular Ising Lattice. II. Occurrence of the Kosterlitz-Thouless-Like Phase Transition

Hajime Takayama, Kazuyuki Matsumoto, Hideaki Kawahara +1 more

A two-dimensional triangular Ising lattice with the nearest-neighbor antiferromagnetic interaction J 1 and the next-nearest-neighbor ferromagnetic interaction - J 2 is studied by the Monte Carlo simulation. It is shown that the system with a finite J 2 undergoes the successive phase transition, paramagnetic→Kosterlitz-Thouless (KT)-like→ferrimagnetic phases, as temperature decreases. The sub-lattice switching phenomenon observed in our previous work is shown to be an intrinsic property inherent to the present system which has an XY character. The marginal exponent of the order-parameter correlation function at the KT-like transition point is seen to increase from 1/4 as the ratio J 2 / J 1 decreases, namely, it reveals a deviation from the universal behavior of a genuine XY model.

Journal of the Physical Society of Japan•Aug 1, 1983•65 citations

Triangular Ising model with nearest- and next-nearest-neighbor couplings in a field

Xiaofeng Qian, Henk W. J. Blöte

The authors study the Ising model on the triangular lattice with nearest-neighbor couplings K(nn) , next-nearest-neighbor couplings K(nnn) >0 , and a magnetic field H . This work is done by means of finite-size scaling of numerical results of transfer matrix calculations, and Monte Carlo simulations. We determine the phase diagram and confirm the character of the critical manifolds. The emphasis of this work is on the antiferromagnetic case K(nn) <0 , but we also explore the ferromagnetic regime K(nn) >/=0 for H=0 . For K(nn) <0 and H=0 we locate a critical phase presumably covering the whole range -infinity< K(nn) <0 . For K(nn) <0 , H not equal 0 we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit H-->infinity this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential.

arXiv:physics/0405055•Physical Review E•Sep 21, 2004•20 citations

A Monte Carlo and renormalization group study of the Ising model with nearest and next nearest neighbor interactions on the triangular lattice

James N. Glosli, Michael Plischke

The Ising model with nearest and next nearest neighbor antiferromagnetic interactions on the triangular lattice displays, for Jnnn/Jnn = 0.1, three phase transitions in different universality classes as the magnetic field is increased. We have studied this model using Monte Carlo and renormalization group techniques. The transition from the paramagnetic to the 2 × 1 phase (universality class of the Heisenberg model with cubic anisotropy) is found to be first order; the transition from the paramagnetic phase to the [Formula: see text] phase (universality class of the three state Potts model) is continuous; and the transition from the paramagnetic to the 2 × 2 phase (universality class of the four state Potts model) is found to change from first order to continuous as the field is increased. We have mapped out the phase diagram and determined the critical exponents for the continuous transitions. A novel technique, using a Landau-like free energy functional determined from Monte Carlo calculations, to distinguish between first order and continuous transitions, is described.

Canadian Journal of Physics•Nov 1, 1983•33 citations

Monte Carlo Simulation of the Antiferromagnetic Ising Model on the Triangular Lattice with the First and Second Neighbour Interactions

Sumiyoshi Fujiki, Keisei Shutoh, Yoshihiko Abe +1 more

Monte Carlo simulations of the Ising model on the triangular lattice with the antiferromagnetic nn interaction J and the ferromagnetic nnn interaction J ' are carried out. Several physical quantities (magnetizations, energies, susceptibilities, specific heats of sublattices and of the total system) are calculated. A phase which resembles the partially disordered phase proposed by Mekata is observed in the finite temperature region. But it is shown in this region that the sublattice magnetizations vanish at the thermodynamic limit and the Kosterlitz-Thouless phase transition is predicted by the finite size analysis.

Journal of the Physical Society of Japan•May 1, 1983•61 citations

PHASE TRANSITIONS IN THE FRUSTRATED ISING MODEL ON TRIANGULAR LATTICE

A.K. Murtazaev, Рамазанов Магомедшейх Курбанович, М. К. Бадиев

Critical properties of an antiferromagnetic Ising model on a triangular lattice with interactions of the next-to-nearest neighbors are investigated by a replica Monte-Carlo method. Using the finite-size scaling theory the static critical exponents of specific heat, ordering parameter, susceptibility, correlation radius as well as the Fisher exponent are calculated.

•Dec 1, 2016•0 citations
Positions of critical temperatures of antiferromagnetic Ising model with ferromagnetic next nearest neighbour interactions on the triangular lattice are investigated by making use of their properties of the Kosterlitz-Thouless type of phase transition. In particular, finite-size scaling method and Monte Carlo Renormalization Group methods (MCRG) with flow diagrams of the anomalous dimension η show the fixed line structure where the correlation length diverges. Another MCRG with flow diagram of the stiffness constant also shows a critical property clearly. The temperature dependence of the long range order is also discussed in order to locate the lower critical point.
The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.
A two-dimensional triangular Ising lattice with the nearest-neighbor antiferromagnetic interaction J 1 and the next-nearest-neighbor ferromagnetic interaction - J 2 is studied by the Monte Carlo simulation. It is shown that the system with a finite J 2 undergoes the successive phase transition, paramagnetic→Kosterlitz-Thouless (KT)-like→ferrimagnetic phases, as temperature decreases. The sub-lattice switching phenomenon observed in our previous work is shown to be an intrinsic property inherent to the present system which has an XY character. The marginal exponent of the order-parameter correlation function at the KT-like transition point is seen to increase from 1/4 as the ratio J 2 / J 1 decreases, namely, it reveals a deviation from the universal behavior of a genuine XY model.
The authors study the Ising model on the triangular lattice with nearest-neighbor couplings K(nn) , next-nearest-neighbor couplings K(nnn) >0 , and a magnetic field H . This work is done by means of finite-size scaling of numerical results of transfer matrix calculations, and Monte Carlo simulations. We determine the phase diagram and confirm the character of the critical manifolds. The emphasis of this work is on the antiferromagnetic case K(nn) <0 , but we also explore the ferromagnetic regime K(nn) >/=0 for H=0 . For K(nn) <0 and H=0 we locate a critical phase presumably covering the whole range -infinity< K(nn) <0 . For K(nn) <0 , H not equal 0 we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit H-->infinity this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential.
The Ising model with nearest and next nearest neighbor antiferromagnetic interactions on the triangular lattice displays, for Jnnn/Jnn = 0.1, three phase transitions in different universality classes as the magnetic field is increased. We have studied this model using Monte Carlo and renormalization group techniques. The transition from the paramagnetic to the 2 × 1 phase (universality class of the Heisenberg model with cubic anisotropy) is found to be first order; the transition from the paramagnetic phase to the [Formula: see text] phase (universality class of the three state Potts model) is continuous; and the transition from the paramagnetic to the 2 × 2 phase (universality class of the four state Potts model) is found to change from first order to continuous as the field is increased. We have mapped out the phase diagram and determined the critical exponents for the continuous transitions. A novel technique, using a Landau-like free energy functional determined from Monte Carlo calculations, to distinguish between first order and continuous transitions, is described.
Monte Carlo simulations of the Ising model on the triangular lattice with the antiferromagnetic nn interaction J and the ferromagnetic nnn interaction J ' are carried out. Several physical quantities (magnetizations, energies, susceptibilities, specific heats of sublattices and of the total system) are calculated. A phase which resembles the partially disordered phase proposed by Mekata is observed in the finite temperature region. But it is shown in this region that the sublattice magnetizations vanish at the thermodynamic limit and the Kosterlitz-Thouless phase transition is predicted by the finite size analysis.