請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90128完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李志煌 | zh_TW |
| dc.contributor.advisor | Jhih-Huang Li | en |
| dc.contributor.author | 馬宗儀 | zh_TW |
| dc.contributor.author | Tsung-Yi Ma | en |
| dc.date.accessioned | 2023-09-22T17:31:47Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-09-22 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-07-19 | - |
| dc.identifier.citation | Michael Aizenman, Hugo Duminil-Copin, and Vladas Sidoravicius. Random currents and continuity of ising model’s spontaneous magnetization. Communications in Mathematical Physics, 334:719–742, 2015.
Francesco Caravenna, Rongfeng Sun, and Nikos Zygouras. Polynomial chaos and scaling limits of disordered systems. Journal of the European Mathematical Society, 19(1):1–65, 2016. Francesco Caravenna, Rongfeng Sun, and Nikos Zygouras. Universality in marginally relevant disordered systems. The Annals of Applied Probability, 27(5):3050–3112, 2017. Dmitry Chelkak, Cl ́ement Hongler, and Konstantin Izyurov. Conformal invariance of spin correlations in the planar ising model. Annals of mathematics, pages 1087 - 1138, 2015. Hugo Duminil-Copin. Parafermionic observables and their applications to planar statistical physics models. Ensaios Matematicos, 25:1–371, 2013. Hugo Duminil-Copin. Random currents expansion of the ising model. arXiv preprint arXiv:1607.06933, 2016. Geoffrey Grimmett. The random-cluster model, volume 333. Springer, 2006. Cl ́ement Hongler. Conformal invariance of ising model correlations. In XVIIth International Congress on Mathematical Physics, pages 326–335. World Scientific, 2014. Ernst Ising. Contribution to the theory of ferromagnetism. Z. Phys, 31(1):253–258, 1925. David Ruelle. Statistical mechanics: Rigorous results. World scientific, 1999. 38 Chen Ning Yang. The spontaneous magnetization of a two-dimensional ising model. Physical Review, 85(5):808, 1952. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90128 | - |
| dc.description.abstract | 易辛模型是一種在統計物理學中用於研究磁鐵材料系統的數學模型。該模型由稱為”自旋”的離散元素組成，可以取兩個不同的值，通常表示為+1和-1。模型考慮了自旋之間的相互作用並考慮了溫度的影響，產生了各種豐富多樣的現象，如相變和臨界現象。
在現實世界的情況下，可能存在外部磁場和磁極之間的干擾。因此，數學家引入了隨機場易辛模型和隨機鍵易辛模型。這些模型分別在與外部磁場和磁極之間相關的項中引入了隨機係數。 | zh_TW |
| dc.description.abstract | The Ising model is a mathematical model employed in statistical physics to investigate systems of ferromagnetic materials. The model consists of discrete elements known as ”spins,” which can assume two distinct values, often represented as +1 and -1.
The model incorporates the interaction between spins and considers the influence of temperature, resulting in a rich variety of phenomena such as phase transitions and critical phenomena. In real-world scenarios, external magnetic fields and disturbances between magnetic poles may exist. Therefore, mathematicians have introduced the Random Field Ising Model (RFIM) and the Random Bond Ising Model (RBIM). These models incorporate random coefficients in the terms related to external magnetic fields and interactions between magnetic poles, respectively. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-09-22T17:31:47Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-09-22T17:31:47Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 致謝 i
中文摘要 ii Abstract iii 1 Outline of thesis 1 2 Definition of Ising Model, Random Field Ising Model and Random Bond Ising Model 2 2.1 Ising Model 2 2.2 Random Field Ising Model and Random Bond Ising Model 3 3 Some Properties of the Ising Model 6 3.1 Critical Temperature and Phase Transition 6 3.2 Useful Inequalities 7 4 Some Useful Expansions of Ising Model 10 4.1 High-Temperature Expansion 10 4.2 Low-Temperature Expansion 12 4.3 Random Current Expansion 13 4.4 Applications 15 4.4.1 Kramers-Wannier Duality 15 4.4.2 Peierls Argument 17 4.4.3 Switching Lemma and the Proof of GKS Inequalities 19 5 Wiener Chaos Expansion 24 6 Random Bond Ising Model on Unit Disc 27 6.1 Motivation and Expansion of the Partition Function for the Random Bond Ising Model 27 6.2 Attempt Under the Assumption of Uniform Bound on Energy Correlation 30 6.3 Attempt Under the Assumption of Uniform Converge on Unit Disc 32 | - |
| dc.language.iso | en | - |
| dc.subject | 高溫展開 | zh_TW |
| dc.subject | 混沌多項式展開 | zh_TW |
| dc.subject | 隨機場易辛模型 | zh_TW |
| dc.subject | 易辛模型 | zh_TW |
| dc.subject | 隨機鍵易辛模型 | zh_TW |
| dc.subject | random field Ising model | en |
| dc.subject | Ising model | en |
| dc.subject | random bond Ising model | en |
| dc.subject | high-temperature expansion | en |
| dc.subject | Wiener chaos expansion | en |
| dc.title | 易辛模型與微擾易辛模型之探討 | zh_TW |
| dc.title | Introduction to the Ising Model and the Ising Model with Disorders | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 林偉傑;陳隆奇 | zh_TW |
| dc.contributor.oralexamcommittee | Wai-Kit Lam;Lung-Chi Chen | en |
| dc.subject.keyword | 易辛模型,隨機場易辛模型,隨機鍵易辛模型,混沌多項式展開,高溫展開, | zh_TW |
| dc.subject.keyword | Ising model,random field Ising model,random bond Ising model,Wiener chaos expansion,high-temperature expansion, | en |
| dc.relation.page | 39 | - |
| dc.identifier.doi | 10.6342/NTU202301483 | - |
| dc.rights.note | 未授權 | - |
| dc.date.accepted | 2023-07-20 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| 顯示於系所單位： | 數學系 | |
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