导　　师： 滕保华

学科专业： 070205

授予学位： 硕士

作　　者： ;

机构地区： 电子科技大学

摘　　要： 铁电性自从在1920年被发现以来就一直被人们所关注。一类具有铁电性质的薄膜材料因为其兼具有压电性、介电性、热释电性、电光效应、声光效应、光折变效应以及非线性光学效应等在应用方面的优良性质,引起了人们广泛的兴趣。本文基于二维伊辛模型,利用蒙特卡洛模拟和平均场近似方法对铁电薄膜的相变性质进行了研究。 /(1/)本文第一章对铁电薄膜的各种应用以及最近的研究现状等做了简要介绍。 /(2/)第二章对相变理论作了介绍,尤其是从几种不同的角度对相变的分类作了较详细的介绍。 /(3/)第三章详细介绍了常用的处理相变的理论方法和基础。对统计物理学的等概率原理这个重要假设作了细致分析。然后简要介绍了伊辛模型,并结合伊辛模型分析了一种用于近似求解的平均场近似理论。另外,从序参量和相变的关系角度对朗道相变理论进行了简要介绍。最后介绍了蒙特卡洛模拟方法的基本原理以及简单抽样和重要性抽样,重点介绍了重要性抽样方法。 /(4/)第四章利用蒙特卡洛方法对二维伊辛模型的相变性质进行了研究。对传统伊辛模型添加了四自旋相互作用,并用参数K表征。利用Metropolis重要性抽样算法研究了系统的平均磁化强度随温度的变化规律,研究了初始位型以及K值对磁化强度随蒙特卡洛步/(mcs/)演化的过程的影响。 /(5/)第五章利用平均场近似方法对在时变正弦外场作用下的伊辛模型的相变性质进行了系统的研究。本工作给出了正弦外场的振幅和频率分别对温度的相图,给出了两类对称性不同的解,并观察到了系统的连续和不连续相变。同时对两种相图下的滞后回线作了系统分析,尤其分析了外加场的频率和振幅对滞回线的影响。 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.

关 键 词： 伊辛模型 蒙特卡洛 四自旋 平均场近似 相图

分 类 号： [O469]

领　　域： [理学] [理学] [理学]