More is different.
God is in the details.
- 講演(21aL3-3) "吸収状態相転移の非平衡臨界点における普遍的スペクトラム構造のテンソル繰り込み群による研究"
- 講演(22pL4-9) "行列積表現を用いたニューラルネットワークのエンタングルメント解析" (共同研究者) 阿蘇品 侑雅（発表）
- 講演(23pA1-1) "テンソルネットワークを用いた量子回路学習" (共同研究者) 真鍋 秀隆（発表）
- May 31, 2021
- StatPhys seminar at University of Tokyo, Hongo, Japan
- Universal spectrum structure on the nonequilibrium critical line of the one-dimensional Domany-Kinzel cellular automaton
The Domany-Kinzel(DK) cellular automaton is a stochastic time-evolutional system with an absorbing state from which the system cannot escape and a canonical model for nonequilibrium critical phenomena. We introduce the tensor network method as a new tool to study it. Estimating the entropy of the DK automaton with a matrix product state representation of distribution, we reported a new cusp of the Renyi entropy in the active phase of the DK cellular automaton. We recently applied a tensor renormalization group method to transfer matrices at the nonequilibrium critical point of the DK cellular automaton, confirming a universal spectrum structure. In this talk, we will report our results with a brief review of models and methods.
 M. Henkel, H. Hinrichsen, and S. Lübeck, Non-Equilibrium Phase Transitions. Volume 1: Absorbing Phase Transitions, Vol. 1 (Springer, 2008).
 K. H. and N. Kawashima, Entropy Governed by the Absorbing State of Directed Percolation, Physical Review Letters 123, 090601 (2019).
 K. H., Universal spectrum structure at nonequilibrium critical points in the (1+1)-dimensional directed percolation, arXiv:2008.10807.
- Critical exponents in coupled phase-oscillator models on small-world networks
- Physical Review E 102, 062212 (2020)
- Ryosuke Yoneda, Kenji Harada, and Yoshiyuki Y. Yamaguchi
- A coupled phase-oscillator model consists of phase oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is widely studied since it describes the synchronization transition, which emerges between the nonsynchronized state and partially synchronized states. The synchronization transition is characterized by several critical exponents, and we focus on the critical exponent defined by coupling strength dependence of the order parameter for revealing universality classes. In a typical interaction represented by the perfect graph, an infinite number of universality classes is yielded by dependency on the natural frequency distribution and the coupling function. Since the synchronization transition is also observed in a model on a small-world network, whose number of links is proportional to the number of oscillators, a natural question is whether the infinite number of universality classes remains in small-world networks irrespective of the order of links. Our numerical results suggest that the number of universality classes is reduced to one and the critical exponent is shared in the considered models having coupling functions up to second harmonics with unimodal and symmetric natural frequency distributions.
- 8 pages, 8 figures
- 講演(9pL1-9) "スモールワールドネットワーク上の結合位相振動子系における同期転移の臨界指数" （共同研究者）米田亮介(発表者), 山口義幸
- 講演(10pL2-7) "同時有向浸透現象の相転移"（共同研究者）星野佑樹(発表者)
- 講演(10pL2-8) "臨界有向浸透現象のスペクトラムを用いた新しい普遍性の提案"
- Kenji Harada
- Using a tensor renormalization group method with oblique projectors for an anisotropic tensor network, we confirm that the rescaled spectrum of transfer matrices at nonequilibrium critical points in the (1+1)-dimensional directed percolation, a canonical model of nonequilibrium critical phenomena, is scale-invariant and its structure is universal.
- 6 pages, 7 figures