More is different.
God is in the details.
- 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
- 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
- Finite-m scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model
- Physical Review E 101, 062111 (2020)
- Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Roman Krčmár, Andrej Gendiar, Seiji Yunoki, and Tomotoshi Nishino
- We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer matrix renormalization group (CTMRG). Scaling analyzes for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension m at the fixed point of CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed point spectrum of the corner transfer matrix in the critical intermediate phase of the six-state clock model is characterized by the scaling dimension consistent with the c=1 boundary conformal field theory associated with the effective Z_6 dual sine-Gordon model.
- 7 pages, 7 figures
- Conference: Tensor Network States: Algorithms and Applications (TNSAA) 2019-2020
- Invited talk: "New numerical approaches for directed percolation"
- Date: Dec. 4, 2019
- Conference dates: Dec. 4-6, 2019
- Venue: NCCU, Taipei, TAIWAN
Monte Carlo simulations
This demonstration shows a Monte Carlo simulation of the two-dimensional Ising model by three algorithms: Metropolis, Swendsen-Wang, and Wolff algorithms.To demo
Assistant Professor, Graduate School of Informatics, Kyoto University, Japan.
Room 203, Research Bldg. No.8, Yoshida Campus, Kyoto Univ., Kyoto, 606-8501, Japan. Map (No.59)