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

Physical Review E

Phase diagram and critical exponent ν for the nearest-neighbor and next-nearest-neighbor interaction Ising model

James L. Monroe, Seung‐Yeon Kim

Published Aug 29, 2007• 30 citations
Publisher

Abstract

We obtain an approximation of the phase diagram of an Ising model with both nearest-neighbor and next-nearest-neighbor interactions on the square lattice. We use the Fisher zeros of the partition functions of a sequence of finite-sized systems along with various extrapolation methods to obtain phase transition points. In addition, we obtain an approximate value of the correlation length critical exponent nu. Our results are compared to previous results for this system using a wide variety of other approaches.

DOI
10.1103/physreve.76.021123

Related papers

Ising Antiferromagnet with Nearest-Neighbor and Next-Nearest-Neighbor Interactions on a Square Lattice

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

The critical properties of two-dimensional antiferromagnetic Ising model in square lattice are investigated using the replica Monte-Carlo method with account of interactions of second nearest neighbors. The diagram of critical temperature dependence on an interaction value of second nearest neighbors is plotted. Static critical exponents of the heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated for this model using the finite-size scaling theory.

Diffusion and defect data, solid state data. Part B, Solid state phenomena/Solid state phenomena•Apr 1, 2014•0 citations

Critical properties of an antiferromagnetic Ising model on a square lattice with interactions of the next-to-nearest neighbors

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

The critical properties of an antiferromagnetic Ising model on a square 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. An analysis of data is performed both with and without taking into account a correction to the finite-size scaling. It was found that in the model under consideration the second order phase transition is observed. It is shown that this model belongs to the new class of universality of critical behavior.

Low Temperature Physics•Dec 1, 2011•24 citations

Phase diagrams and critical behavior of Ising square lattices with nearest-, next-nearest-, and third-nearest-neighbor couplings

D. P. Landau, Kurt Binder

Monte Carlo simulations are used to study the location and nature of phase boundaries for Ising square lattices with antiferromagnetic coupling ${J}_{\mathrm{NN}}$ between nearest neighbors and additional interactions ${J}_{\mathrm{NNN}}$ between next-nearest neighbors and ${J}_{3\mathrm{N}\mathrm{N}}$ between third-nearest neighbors. Results in zero magnetic field are obtained for a wide range of R=${J}_{\mathrm{NNN}/{J}_{\mathrm{NN}}}$ and R'=${J}_{3\mathrm{N}\mathrm{N}/{J}_{\mathrm{NN}}}$. In addition to the c(2\ifmmode\times\else\texttimes\fi{}2) and (2\ifmmode\times\else\texttimes\fi{}1) phases, which also occur for R'=0, we find new (4\ifmmode\times\else\texttimes\fi{}4) and (4\ifmmode\times\else\texttimes\fi{}2) ordered states, for R'\ensuremath{\ne}0, which are separated from the disordered state by lines of first-order transitions. The nonuniversal critical behavior of the (2\ifmmode\times\else\texttimes\fi{}1) phase is studied using the block-distribution method and finite-size scaling. The possible existence of incommensurate phases is also explored.

Physical review. B, Condensed matter•May 1, 1985•202 citations

Phase transitions in the antiferromagnetic ising model on a square lattice with next-nearest-neighbor interactions

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, Felix A. Kassan-Ogly +1 more

The phase transitions in the two-dimensional Ising model on a square lattice are studied using a replica algorithm, the Monte Carlo method, and histogram analysis with allowance for the next-nearest-neighbor interactions in the range 0.1 ≤ r < 1.0. A phase diagram is constructed for the dependence of the critical temperature on the next-nearest-neighbor interaction. A second-order phase transition is detected in this range and the model under study.

Journal of Experimental and Theoretical Physics•Dec 1, 2013•28 citations

Ising-like phase transition in the square lattice fully frustrated XY model with nearest next neighbor couplings

Ren Qing

The Isinglike phase transition in the square lattice fully frustrated XY model with nearest next neighbor (NNN) couplings is studied using the finitesize scaling theory. The critical temperature Tc and static critical exponents 2β/ν and ν are determined. When the NNN coupling variable x=0.5, it is found that in the model exists Isinglike phase transition with the critical temperature Tc=0.404 3±0.000 5 and ν= 0.80±0.05.

Journal of Zhejiang University(Sciences Edition)•Jan 1, 2003•0 citations

Finite-size-scaling estimation of critical exponents in the two-dimensional axial next-nearest-neighbor Ising model

Marcelo D. Grynberg, Horacio Ceva

The magnetic critical exponent of the two-dimensional axial next-nearest-neighbor Ising model is estimated by means of the finite-size scaling of the order parameter. For a finite system without ordering field, this magnitude is computed from the two leading eigenvectors of the transfer matrix. The ferromagnetic-paramagnetic transition temperatures estimated with this method exhibit a small lattice-size dependence. Moreover, they are in good agreement with those obtained using phenomenological renormalization, and also with analytical approximations. The correlation-length critical exponent is calculated by means of phenomenological renormalization. The results found with these numerical techniques indicate that the ferromagnetic-paramagnetic transition of the model seems to be continuous, in contradiction with a previous result obtained using the persistence-length criterion, which indicated that the transition is always first order. We found that the phase transition is first order only when the ratio of the next-nearest-neighbor and nearest-neighbor interactions equals one-half.

Physical review. B, Condensed matter•Nov 1, 1988•6 citations
We obtain an approximation of the phase diagram of an Ising model with both nearest-neighbor and next-nearest-neighbor interactions on the square lattice. We use the Fisher zeros of the partition functions of a sequence of finite-sized systems along with various extrapolation methods to obtain phase transition points. In addition, we obtain an approximate value of the correlation length critical exponent nu. Our results are compared to previous results for this system using a wide variety of other approaches.
The critical properties of an antiferromagnetic Ising model on a square 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. An analysis of data is performed both with and without taking into account a correction to the finite-size scaling. It was found that in the model under consideration the second order phase transition is observed. It is shown that this model belongs to the new class of universality of critical behavior.
Monte Carlo simulations are used to study the location and nature of phase boundaries for Ising square lattices with antiferromagnetic coupling JNN{J}_{\mathrm{NN}}JNN​ between nearest neighbors and additional interactions JNNN{J}_{\mathrm{NNN}}JNNN​ between next-nearest neighbors and J3NN{J}_{3\mathrm{N}\mathrm{N}}J3NN​ between third-nearest neighbors. Results in zero magnetic field are obtained for a wide range of R=JNNN/JNN{J}_{\mathrm{NNN}/{J}_{\mathrm{NN}}}JNNN/JNN​​ and R'=J3NN/JNN{J}_{3\mathrm{N}\mathrm{N}/{J}_{\mathrm{NN}}}J3NN/JNN​​. In addition to the c(2\ifmmode\times\else\texttimes\fi{}2) and (2\ifmmode\times\else\texttimes\fi{}1) phases, which also occur for R'=0, we find new (4\ifmmode\times\else\texttimes\fi{}4) and (4\ifmmode\times\else\texttimes\fi{}2) ordered states, for R'\ensuremath{\ne}0, which are separated from the disordered state by lines of first-order transitions. The nonuniversal critical behavior of the (2\ifmmode\times\else\texttimes\fi{}1) phase is studied using the block-distribution method and finite-size scaling. The possible existence of incommensurate phases is also explored.
The magnetic critical exponent of the two-dimensional axial next-nearest-neighbor Ising model is estimated by means of the finite-size scaling of the order parameter. For a finite system without ordering field, this magnitude is computed from the two leading eigenvectors of the transfer matrix. The ferromagnetic-paramagnetic transition temperatures estimated with this method exhibit a small lattice-size dependence. Moreover, they are in good agreement with those obtained using phenomenological renormalization, and also with analytical approximations. The correlation-length critical exponent is calculated by means of phenomenological renormalization. The results found with these numerical techniques indicate that the ferromagnetic-paramagnetic transition of the model seems to be continuous, in contradiction with a previous result obtained using the persistence-length criterion, which indicated that the transition is always first order. We found that the phase transition is first order only when the ratio of the next-nearest-neighbor and nearest-neighbor interactions equals one-half.