Ferroelectric Thin Films Phase Change Properties Of The Mean Field Approximation And The Monte Carlo Method

The ferroelectricity has been the concern since1920when it is found. A class of thin film materials, having ferroelectric property and also having piezoelectricity effect, pyroelectric effect, electro-optic effect, acousto-optic effect, photorefractive effect, nonlinear optical effect and high dielectric speciality etc. in the application have aroused widespread interest. Based on the two-dimension Ising model, the transition properties is investigated in the frame of Monte Carlo simulation and Mean-field approximation.(1)The first chapter briefly introduce the application in the and the recent research progress of the ferroelectric film.(2)In chapter two, the basic theory of phase transition is introduced in great detail, and especially from several different aspects of the classification.(3)In chapter three, the usual theory method and basic to investigate the phase transition is described. The very important principle of equal probabilities of the statistical physics is analysed carefully and the Ising model is introduced. And then, the Mean-field approximation theory which aims to solve the Ising model is analysed. Also, the Landau phase transition theory is briefly introduced from the relationship between the order parameter and phase transition. Finally, the basic of the Monte Carlo simulation and simple sampling and importance sampling formula is analysed, the importance sampling is focused.(4)Adding on the four-spin interaction,which could be described by a parameter K, the phase transition property of the traditional two-dimension Ising model is investigated using the Monte Carlo method in chapter four. The temperature dependence of the average magnetization of the system is analysed using the Metropolis importance sampling algorithm. The impact of the initial configuration and K to the Monte Carlo step (mcs) dependence of the average magnetization is given.(5)In Chapter five, the phase transition properties for the kinetic Ising model in a sinusoidally oscillating magnetic field are investigated by means of the mean-field calculations. The integrated phase diagrams for not only the amplitude of the oscillating field versus temperature but also the frequency of the oscillating field versus temperature have been calculated respectively, in which the discontinuous and continuous transitions are observed. Meanwhile the hysteresis loops in relation to the two kinds of the phase diagrams have been analyzed systematically, and the effects of the amplitude and the frequency of the oscillating field on the hysteresis loops are illustrated.