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العنوان
ON SOME PROBLEMS OF ISING MODEL IN THE QUANTUM THEORY OF MAGNETISM
الناشر
Zagazig University
المؤلف
Hassan,Samy Hassan Ahmed
الموضوع
ISING MODEL IN THE QUANTUM THEORY MAGNETISM
تاريخ النشر
2004
الفهرس
Only 14 pages are availabe for public view

from 120

from 120

Abstract

This thesis consists of two parts; static and dynamic magnetic properties of random field Ising spin chains. The nearest-neighbour and next-nearest neighbour interactions are taken into consideration. Two distributions of random fields; a binary distribution and a Gaussian distribution, are studied. We consider four cases of the exchange couplings: ferro-ferromagnetic, ferro-antiferromagnetic, antiferro-ferromagnetic and antiferro-antiferromagnetic.
For the static part, the metastable states, their magnetization, energy barriers and their distributions are exactly calculated for different number of spins and for different random fields. There is an exponential growth for the average number of energy minima, but the average of absolute magnetization per spin logarithmically decays, versus number of spins. The distribution of metastable states across their corresponding energy values approaches to the continuous normal distribution. For a weak RF the distribution is a quasi-discrete. Also, the distribution of the magnetized local stable energy minima is a continuous logarithmically decaying with the absolute value of magnetization per spin. The frustration and degeneracy phenomena are discussed for some particular samples.
In the dynamic part, Glauber model is used for chains of N coupled Ising spins in random fields to generate the equations of motion. We dealt with six-spin chains via computer simulations. The relaxation process is analyzed exactly. The number of diverging relaxation times is equal to the number of energy minima minus one. The longest diverging time obeys Arrhenius law, which relates it with the corresponding energy barrier of the ground state. The spectra of relaxation times are shown at different temperatures. The divergent relaxation times are well separated from the convergent ones. The distributions of relaxation times and the corresponding energy barriers are studied exactly. All these distributions are quasi-discrete in the BD case. While in the GD case, they are continuous.
Finally, all the exact results obtained here for both the static and dynamic properties are compared with those of the earlier studied disordered magnetic systems. Our results are in complete agreements with many other Ising models in random field and spin glass systems.