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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 高英哲(Ying-Jer Kao) | |
| dc.contributor.author | Tzu-Chieh Kuo | en |
| dc.contributor.author | 郭子傑 | zh_TW |
| dc.date.accessioned | 2021-05-15T17:54:16Z | - |
| dc.date.available | 2014-07-31 | |
| dc.date.available | 2021-05-15T17:54:16Z | - |
| dc.date.copyright | 2014-07-31 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-07-26 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/5245 | - |
| dc.description.abstract | 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。 | zh_TW |
| dc.description.abstract | 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. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-15T17:54:16Z (GMT). No. of bitstreams: 1 ntu-103-R01222008-1.pdf: 1530447 bytes, checksum: 33f9ceeb93a1e692dbfc5343b4fc8e7e (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 口試委員會審定書 i
致謝iii 中文摘要v Abstract vii Contents ix List of Figures xi List of Tables xiii 1 Introduction 1 2 Theory 3 2.1 Ising model on a square lattice . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 J1 − J2 Ising model on a square lattice . . . . . . . . . . . . . . . . . . . 3 2.3 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.1 Classical Monte Carlo method . . . . . . . . . . . . . . . . . . . 5 2.3.2 Metropolis algorithm . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3.3 Parallel tempering Monte Carlo method . . . . . . . . . . . . . . 7 2.3.4 Calculated observables . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Finite-size scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.5 Non-equilibrium quenching . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5.1 Kibble-Zurek Mechanism . . . . . . . . . . . . . . . . . . . . . 12 2.5.2 Complete finite-size scaling form with linear quench and nonlinear quench . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.6 Statistics and data analysis . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.7 GPU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.7.1 GPU architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.7.2 Algorithm of J1 − J2 Ising model on GPU . . . . . . . . . . . . 25 3 Results 27 3.1 Critical temperatures and critical exponents . . . . . . . . . . . . . . . . 27 3.2 Extraction of the dynamic exponent . . . . . . . . . . . . . . . . . . . . 37 4 Summary and Discussion 41 Bibliography 43 | |
| dc.language.iso | en | |
| dc.title | 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 | zh_TW |
| dc.title | The Quench Dynamics and the Critical Behavior of the J1-J2 Ising Model | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳柏中(Po-Chung Chen),林瑜琤 | |
| dc.subject.keyword | 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, | zh_TW |
| dc.subject.keyword | Classical Monte Carlo,finite-size scaling,GPU,J1?J2 Ising model,quench dynamics,Kibble-Zurek mechanism, | en |
| dc.relation.page | 47 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2014-07-28 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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