【作者】 成明；

【导师】 李炳新；

【作者基本信息】 燕山大学 ， 电路与系统， 2012， 硕士

【摘要】 相变是自然界中广泛存在的一类突变现象，是物质系统由一种稳定状态向另一种稳定状态的跃迁过程，是物理学中极为重要的研究领域。Ising模型是从磁性系统中抽象出来的，描述物质相变与临界现象的一种简单模型。用软件实现Ising模型的模拟速度慢，但用硬件实现具有速度快的特点，因此采用硬件实现Ising模型的模拟具有重要价值和意义。本文主要应用蒙特卡罗方法和元胞自动机方法对Ising模型的研究结果进行分析和总结，用FPGA设计和实现了Ising模型的元胞自动机模拟，并对实验结果进行了对比分析。论文首先介绍了近几年国内外Ising模型的研究现状和一维、二维模型的精确解，分析了在研究三维Ising模型精确解过程中遇到的困难，并用蒙特卡罗数值模拟方法和重整化群方法对Ising模型研究结果进行了总结。其次研究了Ising模型的元胞自动机数值模拟。系统阐述了元胞自动机及对物理系统的模拟，详细介绍了Ising模型的元胞自动机模拟的原理和方法，对用软件实现的二维Ising模型的元胞自动机模拟结果进行了分析和总结，得到了物理系统发生相变及形成宏观磁化的系统能量临界值。最后用原理图输入法和Verilog HDL语言相结合的设计方法实现了一维和二维Ising模型的元胞自动机模拟，并用QuartusII软件进行综合仿真，下载到开发板中。二维仿真结果与用软件方法得到的结果进行比较，结果表明FPGA并行实现Ising模型的速度比用软件方法的速度快。更多还原

【Abstract】 Phase transition, is a kind of break phenomena which exits in the nature widely, is akind of transition process in which substance system changes from one steady state toanother, and is an important research area in Physics. Ising model is abstracted from themagnetic system,which describes a simple model of the material phase transitions andcritical phenomena.Compared to software implementation, implementation throughhardware is faster.Therefore, adopting the method of hardware to complete the simulationof Ising model has a more important value and significance. This paper mainly analyzesthe results of Ising model which is generated by Monte Carlo’s method and cellularautomata method,then designs and realizes the simulation of cellular automata of Isingmodel by FPGA. At last,it compares and analyzes the experiment result.Firstly,it presents domestic and overseas research on Ising model at present and alsointroduces the exact solution to one-dimensional and two-dimensional models,thenanalyzes the difficulties in the study on the exact solution to three-dimensional model.Moreover, numerical simulation method set by Monte Carlo and renormalization groupmethod are used to summarize the results of work on Ising model.Secondly, the numerical simulation of cellular automata of Ising model are discussedin this paper. The cellular automata and simulation of physical systems are formulated.Furthermore, the principles and methods of cellular automata of Ising model are describedin detail. Based on the information obtained from the cellular automata’s simulation resultsof two-dimensional Ising model which achieved through software,this article gets thecritical value of system energy when the phase transformations and macroscopicmagnetization are generated.Finally,with the method combining schematic input method and Verilog HDLlanguage,it achieves the cellular automata’s simulation to one-dimensional andtwo-dimensional models,then uses QuartusⅡ software to realize the comprehensivesimulation and download to the evaluation board. Through the comparison of the resultsbetween two-dimensional simulation and software method,it demonstrates thatimplementation of parallel method is superior to that of software method.更多还原