Thermodynamics of the Ising model in pair approximation

2003 ◽  
Vol 317 (1-2) ◽  
pp. 213-226 ◽  
Author(s):  
T Balcerzak
Keyword(s):  
Ising Model ◽  
Pair Approximation

scholarly journals Origins of the Exchange-Bias Phenomenology, Coercivity Enhancement, and Asymmetric Hysteretic Shearing in Core-Surface Smart Nanoparticles

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Rıza Erdem ◽  
Orhan Yalçın ◽  
Songül Özüm ◽  
Nazire Çiftçi
Keyword(s):  
Particle Size ◽  
Ising Model ◽  
Exchange Bias ◽  
Strong Dependence ◽  
Hysteresis Loops ◽  
Pair Approximation ◽  
Core Surface ◽  
Model Hamiltonian ◽  
Interaction Term ◽  
Experimental Findings

We have used a spin-1 Ising model Hamiltonian with dipolar (bilinear,J), quadrupolar (biquadratic,K), and dipolar-quadrupolar (odd,L) interactions in pair approximation to investigate the exchange-bias (EB), coercive field, and asymmetric hysteretic shearing properties peculiar to core/surface (C/S) composite nanoparticles (NPs). Shifted hysteresis loops with an asymmetry and coercivity enhancement are observed only in the presence of the odd interaction term in the Hamiltonian expression and their magnitudes show strong dependence on the value ofL. The observed coercivity and EB inC/SNPs originated from nonzero odd coupling energies and their dependence on temperature (T) and particle size (R) are also discussed in relation to experimental findings.

THE ISING MODEL STUDIED USING EVOLUTIONARY APPROACH

2005 ◽  
Vol 19 (04) ◽  
pp. 169-179 ◽  
Author(s):  
TOMASZ M. GWIZDAŁŁA
Keyword(s):  
Free Energy ◽  
Solid State ◽  
Ising Model ◽  
Size Effects ◽  
Finite Size ◽  
Evolutionary Approach ◽  
Pair Approximation ◽  
Global Minima ◽  
Finite Size Effects ◽  
The One

Evolutionary algorithms are very powerful techniques for the search of global minima. In this work we want to present the evolutionary approach to the one of the most fundamental problems of solid state magnetism: the Ising model. For the samples built in the most simple way, i.e. only from the ±1 spins, various temperature characteristics coming from the minimization of Gibbs free energy with entropy calculated from the pair approximation are shown. The calculations have been performed for samples of different magnitude which allowed the consideration of finite size effects.

q-Neighbor Ising model on random networks

2018 ◽  
Vol 29 (06) ◽  
pp. 1850041 ◽  
Author(s):  
A. Chmiel ◽  
T. Gradowski ◽  
A. Krawiecki
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Ising Model ◽  
Random Graphs ◽  
Quantitative Agreement ◽  
Pair Approximation ◽  
Random Networks ◽  
Kinetic Ising Model ◽  
Discontinuous Transition ◽  
The Mean

A modified kinetic Ising model with Metropolis dynamics, so-called [Formula: see text]-neighbor Ising model, is investigated on random graphs. In this model, each spin interacts only with [Formula: see text] spins randomly chosen from its neighborhood. Investigations are performed by means of Monte Carlo (MC) simulations and the analytic pair approximation (PA). The range of parameters such as the size of the [Formula: see text]-neighborhood and the mean degree of nodes of the random graph is determined for which the model exhibits continuous or discontinuous ferromagnetic (FM) phase transition with decreasing temperature. It is also shown that, in the case of discontinuous transition for large enough and fixed mean degree of nodes, the width of the hysteresis loop oscillates with the parameter [Formula: see text], expanding for even and shrinking for odd values of [Formula: see text]. Predictions of the PA show satisfactory quantitative agreement with results of MC simulations.

COMPETING DYNAMICAL BEHAVIOR OF THE ISING MODEL IN ONE DIMENSION

1996 ◽  
Vol 10 (20) ◽  
pp. 945-953 ◽  
Author(s):  
B.C.S. GRANDI ◽  
W. FIGUEIREDO
Keyword(s):  
Ising Model ◽  
Dynamical Behavior ◽  
Heat Bath ◽  
External Source ◽  
One Dimension ◽  
Pair Approximation ◽  
One Dimensional ◽  
Ferromagnetic Ising Model ◽  
The One ◽  
Competition Parameter

We have studied the behavior of the one-dimensional ferromagnetic Ising model in contact with a heat bath and subject to an external source of energy. The contact with the heat bath is simulated by a process of Glauber type, while the continuous flux of energy into the system by a process of Kawasaki type. We show, within the dynamical pair approximation that the phase diagram exhibits a line of continuous nonequilibrium transitions between the paramagnetic and antiferromagnetic phases. However, detailed Monte Carlo simulations on the same model show clearly that the only stationary state is the paramagnetic one, whatever is the value of the competition parameter between the Glauber and Kawasaki dynamics.

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