- 作者: 胡進錕
- 中文摘要: 許多相變問題可由晶格上易行類模型或硬核粒子模型表示。展透與碎形是近數十年來廣泛用於許多科學部門的幾何 觀念。本論文回顧我們用展透和碎形觀念以了解和描述易行類模型和硬核粒子模型的相變行?。討論的題材包括:1.展 透和碎形觀念的重要發展,2.易行類模型的展透理論,3.以展透重整群法計算Potts模型之自由能、臨界點、臨界指數 、碎形維度、秩序參數等量,4.以展透蒙地卡羅模擬法計算Potts模型的物理量,5.展透與硬核粒子相變的關連。本論 文也?明一些?得進一?研究的問題。
- 英文摘要: Many phase transition problems may be represented by Ising-type models or hard-core particle models on lattices. Percolation and fractals are geometrical concepts which have been used widely in many branches of sciences in recent decades. In this paper we review the usefulness of percolation and fractals in our understanding and description of phase transitions of Ising-type and hard-core particle models. The topics under discussion include (1). important developments of percolation and fractals as mathematical concepts, (2). percolation theory of phase transitions of Ising-type models, (3). percolation renorma-lization group calculations of free energies, critical points, critical exponents, fractal dimensions, order parameters, etc. for the Potts models, (4). percolation Monte Carlo calculations of physical quantities for the Potts models, and (5). connections between percolation and phase transitions of hard-core particles. Some problems for future research are also discussed.
- 中文關鍵字: percolation; fractals; phase transitions; renormalization group
- 英文關鍵字: --