基于FPGA的混合自旋钻石链Ising模型的蒙特卡洛模拟
发布时间：2018-07-28 14:08
【摘要】：Ising模型凭借它简单的结构和丰富的内涵等优点在物理统计中得到广泛的应用,研究混合自旋钻石链Ising模型的磁性质对于一些具有自旋阻挫效应的化合物材料的实验和应用研究有一定的指导意义,Ising模型的数值模拟需要大量的计算工作,微型计算机由于受到总线位宽的限制,其计算所需时间会相对较长;FPGA凭借其在并行计算方面的显著优势可以大大缩短模拟Ising模型所需要的时间。首先,本文对一维钻石链状Ising模型进行了理论介绍,并通过探讨蒙特卡洛方法对该模型的模拟,设计总结出模型的硬件实现方法,使得模型状态能够进行并行更新。其次,本文以FPGA为平台,使用Verilog硬件描述语言设计并实现了根据能量变换来更新自旋状态的一维钻石链Ising模型,在设计过程中,由于模型中格点数量庞大,占用资源过多,为节省资源本文采用串并联结合的设计方法,既使得模型更新速度得到提升,又节省了逻辑资源。然后,为方便对Ising模型的数据进行分析研究,本文设计了一个围绕模型的一个系统。系统包括数据产生模块,存储模块,数据处理模块和控制模块。系统的核心部分是数据产生模块,也就是Ising模型的功能仿真模块,在每个时钟沿存储器模块都会存储所有自旋的当前状态,数据处理模块从存储模块读入并处理数据;最后通过传输模块将数据通过URAT传输到计算机并显示出来。上述的整个过程都是由控制模块控制各个模块的使能端将数据进行有序的传输的。最后,本文对一维钻石链状Ising模型在FPGA上的功能实现和数据的传输的总体方案以及各个模块的软硬件实现进行了详尽的描述,并通过与在微型计算机上的模拟进行比较,证明Ising模型在FPGA上的状态更新速度是在普通计算机上的上百倍。
[Abstract]:Ising model is widely used in physical statistics by virtue of its simple structure and rich connotation. The study of the magnetic properties of the mixed spin diamond chain Ising model has a certain guiding significance for the experimental and applied study of some compound materials with spin buckling effect. The numerical simulation of the Ising model requires a lot of computational work. Due to the limitation of bus bit width, the computing time of microcomputer is relatively long. With its remarkable advantage in parallel computing, the time required to simulate Ising model can be greatly shortened. Firstly, the one-dimensional diamond chain Ising model is introduced theoretically, and the simulation of the model by Monte Carlo method is discussed. The hardware implementation method of the model is designed and summarized, which enables the model state to be updated in parallel. Secondly, based on FPGA and Verilog hardware description language, the one-dimensional diamond chain Ising model is designed and implemented to update the spin state according to the energy transformation. In the design process, because of the large number of lattice points in the model, it takes up too much resources. In order to save resources, this paper adopts the design method of series-parallel connection, which not only improves the updating speed of the model, but also saves the logical resources. Then, in order to analyze and study the data of Ising model, a system around the model is designed in this paper. The system includes a data generation module, a storage module, a data processing module and a control module. The core of the system is the data generation module, which is the function simulation module of the Ising model. The current state of all spin is stored in each clock along the memory module, and the data processing module reads in and processes the data from the storage module. Finally, the data is transmitted to the computer through URAT and displayed through the transmission module. The whole process is controlled by the control module. Finally, this paper describes in detail the function realization of one-dimensional diamond chain Ising model on FPGA, the overall scheme of data transmission and the hardware and software implementation of each module, and compares it with the simulation on microcomputer. It is proved that the state update speed of Ising model on FPGA is hundreds of times faster than that on ordinary computer.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN791
本文编号：2150460
[Abstract]:Ising model is widely used in physical statistics by virtue of its simple structure and rich connotation. The study of the magnetic properties of the mixed spin diamond chain Ising model has a certain guiding significance for the experimental and applied study of some compound materials with spin buckling effect. The numerical simulation of the Ising model requires a lot of computational work. Due to the limitation of bus bit width, the computing time of microcomputer is relatively long. With its remarkable advantage in parallel computing, the time required to simulate Ising model can be greatly shortened. Firstly, the one-dimensional diamond chain Ising model is introduced theoretically, and the simulation of the model by Monte Carlo method is discussed. The hardware implementation method of the model is designed and summarized, which enables the model state to be updated in parallel. Secondly, based on FPGA and Verilog hardware description language, the one-dimensional diamond chain Ising model is designed and implemented to update the spin state according to the energy transformation. In the design process, because of the large number of lattice points in the model, it takes up too much resources. In order to save resources, this paper adopts the design method of series-parallel connection, which not only improves the updating speed of the model, but also saves the logical resources. Then, in order to analyze and study the data of Ising model, a system around the model is designed in this paper. The system includes a data generation module, a storage module, a data processing module and a control module. The core of the system is the data generation module, which is the function simulation module of the Ising model. The current state of all spin is stored in each clock along the memory module, and the data processing module reads in and processes the data from the storage module. Finally, the data is transmitted to the computer through URAT and displayed through the transmission module. The whole process is controlled by the control module. Finally, this paper describes in detail the function realization of one-dimensional diamond chain Ising model on FPGA, the overall scheme of data transmission and the hardware and software implementation of each module, and compares it with the simulation on microcomputer. It is proved that the state update speed of Ising model on FPGA is hundreds of times faster than that on ordinary computer.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN791
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相关期刊论文 前3条
1 李立奇;王宗笠;;二维微正则Ising模型临界相变的Q2R方法[J];重庆大学学报(自然科学版);2006年11期
2 韩旭;郑磊;;基于FPGA的任意波形发生器的设计与实现[J];电子测量技术;2013年07期
3 周庆;黄党志;;基于Ising模型的QR码加密算法[J];计算机应用;2013年10期
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