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

Chinese Journal of Physics

Magnetic Phase Transitions in Systems with Competing Interactions

David Paul Landau

Published Jul 1, 1977• 2 citations
OpenAlex

Abstract

Phase transitions in magnetic systems are studied using a Monte Carlo computer simulation method. The fundamentals of the technique are described and the strengths and limitations of this approach are discussed. Comparisons are made between the Monte Carlo data and exact results for the Ising square lattice. The properties of several different types of anisotropic systems are determined with particular care taken near the critical temperature Tc Competing interactions between neighboring sites has the effect of shifting Tc and may, in some cases, even change the nature of the ordered magnetic state. Critical field boundaries are traced out for several antiferromagnets and we show how competing interactions may give rise to tricritical points. We also present data on systems with impurities and examine the effects of free surfaces on the phase transition. Lastly we show how the transformation from the 2-dim Ising model to its lattice-gas model equivalent allows us to study adsorbed gas monolayers.

Related papers

Magnetic Properties of a Square Lattice Ising Ferromagnetic System for Different Spins with Monte Carlo Simulation

A. Azdouh, Said Harir, Anouar Elidrysy +3 more

Using the Monte Carlo Simulation (MCS) method combined with the Metropolis algorithm, we explore the magnetic properties of a two-dimensional (2D) spin system with spins 1, 2 and 3. The adapted simulation to the Ising model aims to study the impact of the correction term a of the interaction with second neighbors and the crystal field D on the critical temperature [Formula: see text] of the 2D anisotropic square lattice for different integer values of spins. The obtained results demonstrate that the critical temperature [Formula: see text] is significantly affected by the competing interactions between the anisotropy parameter, second-neighbor interaction and the crystal field. The considered model exhibits a critical phase transition regardless of the spin S value where the critical temperature increases with the value of S. Note that this phase transition occurs under the condition [Formula: see text]. Moreover, the obtained results show that the complex interactions give rise to a variety of phase diagrams, thereby revealing the richness of possible magnetic behaviors in the studied system.

SPIN•Feb 12, 2025•1 citation

Phase Transitions of Random Binary Magnetic Square Lattice Ising Systems

I. Q. Sikakana

Binary magnetic square lattice Ising system with nearest neighbour interactions were simulated using the Monte Carlo technique. Two types of ions were randomly distributed on the lattice sites, one type interacting ferromagnetic and the other antiferromagnetic. A phase diagram of the ion concentration dependent critical temperature, Tc was deduced. Combined Bethe Peierls approximation and Mean Field theory phase transition results were compared to the results of the present method. An improved accuracy of the approximations of the critical temperatures was observed. The Monte Carlo simulation is thus shown to be a more reliable method for obtaining the physical properties of the random binary two-dimensional Ising system. Keywords: Binary magnetic two-dimensional Ising system, phase transition, Monte Carlo simulations

arXiv:1301.2400•Jan 11, 2013•0 citations

Monte Carlo studies of the Ising square lattice with competing interactions

Ansgar Kalz, A. Honecker, Sebastian Fuchs +1 more

Abstract. We use improved Monte-Carlo algorithms to study the antiferromagnetic 2D-Ising model with competing interactions J1 on nearest neighbour and J2 on next-nearest neighbour bonds. The finite-temperature phase diagram is divided by a critical point at J2 = J1/2 where the groundstate is highly degenerate. To analyse the phase boundaries we look at the specific heat and the energy distribution for various ratios of J2/J1. We find a first order transition for small J2> J1/2 and the transition temperature suppressed to TC = 0 at the critical point. 1.

•Aug 3, 2013•22 citations

Frustrations and phase transitions in the Ising model on square lattice

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

The phase transitions in two-dimensional antiferromagnetic Ising model are studied on a square lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transition of second order and the frustration points depending on relative interaction values and magnetic field. A effect, heat capacity splitting near the frustration points, is found.

Journal of Physics Conference Series•May 15, 2014•5 citations

Phase diagram and critical behavior of the square-lattice Ising model with competing nearest-neighbor and next-nearest-neighbor interactions

Junqi Yin, David Paul Landau

Using the parallel tempering algorithm and graphics processing unit accelerated techniques, we have performed large-scale Monte Carlo simulations of the Ising model on a square lattice with antiferromagnetic (repulsive) nearest-neighbor and next-nearest-neighbor interactions of the same strength and subject to a uniform magnetic field. Both transitions from the (2x1) and row-shifted (2x2) ordered phases to the paramagnetic phase are continuous. From our data analysis, re-entrance behavior of the (2x1) critical line and a bicritical point which separates the two ordered phases at T=0 are confirmed. Based on the critical exponents we obtained along the phase boundary, Suzuki's weak universality seems to hold.

arXiv:0909.4000•Physical Review E•Nov 17, 2009•44 citations

Monte Carlo Studies of the Square Lattice Ising System with the Two-Dimensional Dipolar Interaction

Seizo Watarai, Keizô Yamamoto, Akira Nakanishi

Monte Carlo simulations are performed on the square lattice Ising system with both the nearest neighbor and the two-dimensional dipolar interactions in order to investigate the critical property of ferromagnetic phase transitions in this 2-dimensional system. Applying the finite size scaling theory to Monte Carlo data just near the transition point, the critical indices of this dipolar system are calculated and α=0.31±0.04, β =0.20±0.02, γ=1.08±0.20 and ν=0.72±0.10 are obtained. However, in the temperature region considerably far from the transition point, different values of α, β and γ seem to be adequate, which are rather close to those of the rigorous result of the 2-dimensional Ising model.

Journal of the Physical Society of Japan•May 15, 1992•0 citations
Phase transitions in magnetic systems are studied using a Monte Carlo computer simulation method. The fundamentals of the technique are described and the strengths and limitations of this approach are discussed. Comparisons are made between the Monte Carlo data and exact results for the Ising square lattice. The properties of several different types of anisotropic systems are determined with particular care taken near the critical temperature Tc Competing interactions between neighboring sites has the effect of shifting Tc and may, in some cases, even change the nature of the ordered magnetic state. Critical field boundaries are traced out for several antiferromagnets and we show how competing interactions may give rise to tricritical points. We also present data on systems with impurities and examine the effects of free surfaces on the phase transition. Lastly we show how the transformation from the 2-dim Ising model to its lattice-gas model equivalent allows us to study adsorbed gas monolayers.
Using the Monte Carlo Simulation (MCS) method combined with the Metropolis algorithm, we explore the magnetic properties of a two-dimensional (2D) spin system with spins 1, 2 and 3. The adapted simulation to the Ising model aims to study the impact of the correction term a of the interaction with second neighbors and the crystal field D on the critical temperature [Formula: see text] of the 2D anisotropic square lattice for different integer values of spins. The obtained results demonstrate that the critical temperature [Formula: see text] is significantly affected by the competing interactions between the anisotropy parameter, second-neighbor interaction and the crystal field. The considered model exhibits a critical phase transition regardless of the spin S value where the critical temperature increases with the value of S. Note that this phase transition occurs under the condition [Formula: see text]. Moreover, the obtained results show that the complex interactions give rise to a variety of phase diagrams, thereby revealing the richness of possible magnetic behaviors in the studied system.
Binary magnetic square lattice Ising system with nearest neighbour interactions were simulated using the Monte Carlo technique. Two types of ions were randomly distributed on the lattice sites, one type interacting ferromagnetic and the other antiferromagnetic. A phase diagram of the ion concentration dependent critical temperature, Tc was deduced. Combined Bethe Peierls approximation and Mean Field theory phase transition results were compared to the results of the present method. An improved accuracy of the approximations of the critical temperatures was observed. The Monte Carlo simulation is thus shown to be a more reliable method for obtaining the physical properties of the random binary two-dimensional Ising system. Keywords: Binary magnetic two-dimensional Ising system, phase transition, Monte Carlo simulations
Abstract. We use improved Monte-Carlo algorithms to study the antiferromagnetic 2D-Ising model with competing interactions J1 on nearest neighbour and J2 on next-nearest neighbour bonds. The finite-temperature phase diagram is divided by a critical point at J2 = J1/2 where the groundstate is highly degenerate. To analyse the phase boundaries we look at the specific heat and the energy distribution for various ratios of J2/J1. We find a first order transition for small J2> J1/2 and the transition temperature suppressed to TC = 0 at the critical point. 1.
The phase transitions in two-dimensional antiferromagnetic Ising model are studied on a square lattice by taking the interactions of next-nearest neighbors into account. The model is investigated on basis of the replica Monte Carlo algorithm and the histogrammic analysis of data. The diagram of the critical temperature dependence on an interaction value of next-nearest neighbors is plotted. The studied model reveals the phase transition of second order and the frustration points depending on relative interaction values and magnetic field. A effect, heat capacity splitting near the frustration points, is found.
Using the parallel tempering algorithm and graphics processing unit accelerated techniques, we have performed large-scale Monte Carlo simulations of the Ising model on a square lattice with antiferromagnetic (repulsive) nearest-neighbor and next-nearest-neighbor interactions of the same strength and subject to a uniform magnetic field. Both transitions from the (2x1) and row-shifted (2x2) ordered phases to the paramagnetic phase are continuous. From our data analysis, re-entrance behavior of the (2x1) critical line and a bicritical point which separates the two ordered phases at T=0 are confirmed. Based on the critical exponents we obtained along the phase boundary, Suzuki's weak universality seems to hold.
Monte Carlo simulations are performed on the square lattice Ising system with both the nearest neighbor and the two-dimensional dipolar interactions in order to investigate the critical property of ferromagnetic phase transitions in this 2-dimensional system. Applying the finite size scaling theory to Monte Carlo data just near the transition point, the critical indices of this dipolar system are calculated and α=0.31±0.04, β =0.20±0.02, γ=1.08±0.20 and ν=0.72±0.10 are obtained. However, in the temperature region considerably far from the transition point, different values of α, β and γ seem to be adequate, which are rather close to those of the rigorous result of the 2-dimensional Ising model.