数学を使おう！フォーラムで楽しくお話してみませんか？
【投稿日】2013.3.11
| 日時： | 2013年3月11日㈪ 15:00−17:00 |
|---|---|
| 場所： | 青葉山キャンパス 情報科学研究科棟 2階中講義室 |
| 世話人： | 長谷川雄央 |
15:00−15:50
Masayuki Ohzeki (Kyoto Univ.)
Duality with real-space renormalization and its application to bond percolation
We obtain the exact solution of the bond-percolation thresholds with inhomogeneous probabilities on the square lattice. Our method is based on the duality analysis with real-space renormalization, which is a profound technique invented in the spin-glass theory. The resultant generic formulas from our derivation can give several estimations for the bond-percolation thresholds on other lattices as the Kagome and bow-tie lattices. Ref: Phys. Rev. E 87, 012137 (2013)
16:10−17:00
Stefan Boettcher (Emory Univ.)
Real-Space Renormalization Group for Hierarchical Networks and Quantum Walks
An elementary introduction of the venerable real-space renormalization group (RG) for regular lattices will be provided. Then, RG will be discussed on hierarchical networks for models such as percolation and the Ising model. A simple, generic description is provided for the unusual critical behavior found on such networks. Time permitting, the application of RG to transport problems is described by example of random walks, which we have recently generalized into a unified treatment of classical, persistent, and quantum walks. The study of RG for quantum walks is particularly challenging because it requires the extension of the RG-flow equations into the complex plane.
