二維易辛模型考慮次近鄰交互作用其相變化及淬火動力學

The Quench Dynamics and the Critical Behavior of the J1-J2 Ising Model

郭子傑(Tzu-Chieh Kuo)

指導教授 ： 高英哲

國立臺灣大學/理學院/物理研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.02767

摘要

於圖形處理單元(GPU) 環境中使用平行演算法及蒙地卡羅演算法模擬了二維方格易辛模型並考慮次近鄰之交互作用，其中最近鄰(J1) 與次近鄰(J2) 之交互作用皆為反鐵磁性且互為競爭關係，本篇展現了如何計算出臨界指數與交互作用比例(J2/J1) 之關係，及利用Metropolis演算法模擬非平衡淬火至臨界溫度並計算出動力學指數。

關鍵字

古典蒙地卡羅演算法 ； 有限尺度效應 ； 圖形處理單元 ； 二維方格易辛模型考慮次近鄰之交互作用 ； 淬火動力學 ； Kibble-Zurek機制

並列摘要

We perform the Monte Carlo simulations of the J1 −J2 (frustrated) Ising model on a square lattice with competing coupling J1 > 0 (nearest-neighbor, anti-ferromagnetic) and J2 > 0 (next-nearest neighbor, also anti-ferromagnetic) using the graphic processing unit (GPU). In this thesis, we present the critical exponents evolution as one tunes J2/J1 and the extraction of the dynamical exponent using non-equilibrium quenching with Metropolis algorithm to the critical point.

並列關鍵字

Classical Monte Carlo ； finite-size scaling ； GPU ； J1−J2 Ising model ； quench dynamics ； Kibble-Zurek mechanism

參考文獻

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