【摘要】：Ising模型憑借它簡單的結構和豐富的內涵等優(yōu)點在物理統(tǒng)計中得到廣泛的應用,研究混合自旋鉆石鏈Ising模型的磁性質對于一些具有自旋阻挫效應的化合物材料的實驗和應用研究有一定的指導意義,Ising模型的數(shù)值模擬需要大量的計算工作,微型計算機由于受到總線位寬的限制,其計算所需時間會相對較長;FPGA憑借其在并行計算方面的顯著優(yōu)勢可以大大縮短模擬Ising模型所需要的時間。首先,本文對一維鉆石鏈狀Ising模型進行了理論介紹,并通過探討蒙特卡洛方法對該模型的模擬,設計總結出模型的硬件實現(xiàn)方法,使得模型狀態(tài)能夠進行并行更新。其次,本文以FPGA為平臺,使用Verilog硬件描述語言設計并實現(xiàn)了根據(jù)能量變換來更新自旋狀態(tài)的一維鉆石鏈Ising模型,在設計過程中,由于模型中格點數(shù)量龐大,占用資源過多,為節(jié)省資源本文采用串并聯(lián)結合的設計方法,既使得模型更新速度得到提升,又節(jié)省了邏輯資源。然后,為方便對Ising模型的數(shù)據(jù)進行分析研究,本文設計了一個圍繞模型的一個系統(tǒng)。系統(tǒng)包括數(shù)據(jù)產(chǎn)生模塊,存儲模塊,數(shù)據(jù)處理模塊和控制模塊。系統(tǒng)的核心部分是數(shù)據(jù)產(chǎn)生模塊,也就是Ising模型的功能仿真模塊,在每個時鐘沿存儲器模塊都會存儲所有自旋的當前狀態(tài),數(shù)據(jù)處理模塊從存儲模塊讀入并處理數(shù)據(jù);最后通過傳輸模塊將數(shù)據(jù)通過URAT傳輸?shù)接嬎銠C并顯示出來。上述的整個過程都是由控制模塊控制各個模塊的使能端將數(shù)據(jù)進行有序的傳輸?shù)�。最�?本文對一維鉆石鏈狀Ising模型在FPGA上的功能實現(xiàn)和數(shù)據(jù)的傳輸?shù)目傮w方案以及各個模塊的軟硬件實現(xiàn)進行了詳盡的描述,并通過與在微型計算機上的模擬進行比較,證明Ising模型在FPGA上的狀態(tài)更新速度是在普通計算機上的上百倍。
[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.
【學位授予單位】：燕山大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TN791

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本文編號：2150460