Transitions between modulated phases in an Ising model with third-neighbour interactions (mean-field approximation)

1999 ◽  
Vol 192 (3) ◽  
pp. 505-515 ◽  
Author(s):  
Vittorio Massidda
Keyword(s):  
Ising Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Modulated Phases

PHASE TRANSITIONS OF THE MIXED-SPIN ISING MODEL ON A DECORATED LATTICE WITH THE NEAREST-NEIGHBOR INTERACTION BETWEEN DECORATING SPINS

2009 ◽  
Vol 23 (24) ◽  
pp. 4963-4976 ◽  
Author(s):  
A. BENYOUSSEF ◽  
A. EL KENZ ◽  
M. EL YADARI ◽  
M. LOULIDI
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Phase Diagrams ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Nearest Neighbors ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Neighbor Interaction ◽  
Mixed Spin

A mean-field approximation is developed for a decorated ferrimagnetic Ising model, in which the two magnetic atoms A and B have spins σ=1/2 and S=1, respectively. In this system, the exchange interaction between nearest-neighbors of atom B is taken into account. Some interesting phenomena, such as the appearance of three types of phase diagrams and the existence of one and two compensation points are found. Phase diagrams and temperature dependence of the magnetizations of the system are investigated in detail.

Phase Transitions and the Ising Model

2019 ◽  
pp. 423-446
Author(s):  
Robert H. Swendsen
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Landau Theory ◽  
Magnetic Moments ◽  
Mean Field ◽  
Higher Dimensions ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ising Chain ◽  
The Mean

Chapter 17 presented one example of a phase transition, the van der Waals gas. This chapter provides another, the Ising model, a widely studied model of phase transitions. We first give the solution for the Ising chain (one-dimensional model), including the introduction of the transfer matrix method. Higher dimensions are treated in the Mean Field Approximation (MFA), which is also extended to Landau theory. The Ising model is deceptively simple. It can be defined in a few words, but it displays astonishingly rich behavior. It originated as a model of ferromagnetism in which the magnetic moments were localized on lattice sites and had only two allowed values.

The Glauber and Metropolis Transition Rates on the Stationary States of the Ising Model

1997 ◽  
Vol 11 (13) ◽  
pp. 565-570
Author(s):  
G. L. S. Paula ◽  
W. Figueiredo
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Two Dimensions ◽  
Mean Field Approximation ◽  
Stationary States ◽  
Transition Rates ◽  
The Mean ◽  
The One

We have applied the Glauber and Metropolis prescriptions to investigate the stationary states of the Ising model in one and two dimensions. We have employed the formalism of the master equation to follow the evolution of the system towards the stationary states. Although the Glauber and Metropolis transition rates lead the system to the same equilibrium states for the Ising model in the Monte Carlo simulations, we show that they can predict different results if we disregard the correlations between spins. The critical temperature of the one-dimensional Ising model cannot even be found by using the Metropolis algorithm and the mean field approximation. However, taking into account only correlations between nearest neighbor spins, the resulting stationary states become identical for both Glauber and Metropolis transition rates.

Modulated Phases on the FCC(110) Surfaces with Adsorbate-Induced Reconstructions

2003 ◽  
Vol 10 (02n03) ◽  
pp. 189-194
Author(s):  
Min Kang ◽  
Makoto Kaburagi
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Correlation Function ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Modulated Phases ◽  
The Mean ◽  
Beg Model

We theoretically investigate the fcc(110) surfaces with missing row reconstructions induced by adatoms using the Blume–Emmery–Griffith (BEG) model. In the model, Kij is introduced to denote interactions between surface atoms and Jij to describe interactions between dipoles. The investigation by the mean field approximation has predicted that there appear modulated phases on the surfaces as the next-nearest-neighbor (NNN) and the nearest-neighbor (NN) interactions along the [001] direction become competitive. In this study, Monte Carlo simulations are performed to confirm the prediction. A correlation function defined by concentration operators in wave vector q space is calculated. The results show that the concentration modulations appear. The temperature versus the ratio of the NNN interaction K2 to the NN interaction K1 phase diagram is obtained. The possible features of the modulated phases in experiments are discussed.

STOCHASTIC RESONANCE IN THE ISING MODEL ON A BARABÁSI–ALBERT NETWORK

2004 ◽  
Vol 18 (12) ◽  
pp. 1759-1770 ◽  
Author(s):  
A. KRAWIECKI
Keyword(s):  
Ising Model ◽  
Stochastic Resonance ◽  
Spectral Power ◽  
Strong Dependence ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ferromagnetic Phase ◽  
Periodic Signal ◽  
Power Amplification

Stochastic resonance is investigated in the Ising model with ferromagnetic coupling on a Barabási–Albert network, subjected to weak periodic magnetic field. Spectral power amplification as a function of temperature shows strong dependence on the number of nodes, which is related to the dependence of the critical temperature for the ferromagnetic phase transition, and on the frequency of the periodic signal. Double maxima of the spectral power amplification evaluated from the time-dependent magnetization are observed for intermediate frequencies of the periodic signal, which are also dependent on the number of nodes. In the thermodynamic limit, the height of the maxima decreases to zero and stochastic resonance disappears. Results of numerical simulations are in qualitative agreement with predictions of the linear response theory in the mean-field approximation.

The Curie Temperature of the Ferroelectric Superlattice Films with Surface Modification

2009 ◽  
Vol 64 (11) ◽  
pp. 723-728
Author(s):  
Bao-Bing Zheng ◽  
Xiao-Yu Kuang ◽  
Shao-Mei Chang ◽  
Ya-Ru Zhao ◽  
Wen-Qiang Li
Keyword(s):  
Surface Modification ◽  
Ising Model ◽  
Mean Field ◽  
Transverse Field ◽  
Exchange Interactions ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Model Parameters ◽  
Transverse Ising Model ◽  
The Mean

We examine the critical behaviour of a finite alternating ferroelectric superlattice based on the transverse Ising model within the framework of the mean-field approximation. The results indicate that the features of the phase diagrams can be greatly modified by changing the transverse Ising model parameters. The transition temperature of alternating superlattice is described as function of the inter- and intra-layer exchange interactions, the strength of the transverse field, the superlattice thickness and the polarizations. In addition, the effects of surface modification on finite superlattices are also studied.

A MEAN FIELD APPROACH FOR ISING MODELS ON SCALE-FREE NETWORKS

2011 ◽  
Vol 25 (07) ◽  
pp. 453-464 ◽  
Author(s):  
G. IANNONE ◽  
ORLANDO LUONGO
Keyword(s):  
Ising Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Practical Applications ◽  
Scale Free ◽  
Wide Range ◽  
Scale Free Networks ◽  
The Mean ◽  
Mean Field Approximations

Recently, the study of complex networks led to the analysis of the so-called scale-free models in statistical mechanics. This study has increased its importance, thanks to the wide range of applications in numerous physical contexts; for example, one important question is to understand the behavior of various models on such networks. We start first by investigating the Ising model in the mean field approximation and on scale-free networks, studying especially the Ising model with annealed dilution and Clock model, with particular attention devoted to focusing on similarities between the mean field approximations with or without scale-free statistics. A particular emphasis is given to the possible practical applications of these results in other disciplines such as medicine and social science.

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