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Stability of energy landscape for Ising models
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| Title: | Stability of energy landscape for Ising models |
| Authors: | Fukushima-Kimura, Bruno Hideki Browse this author | | Sakai, Akira Browse this author →KAKEN DB | | Toyokawa, Hisayoshi Browse this author | | Ueda, Yuki Browse this author |
| Keywords: | Stability | | Spin glass | | Ising model | | Ground states |
| Issue Date: | 1-Dec-2021 |
| Publisher: | Elsevier |
| Journal Title: | Physica A: Statistical Mechanics and its Applications |
| Volume: | 583 |
| Start Page: | 126208 |
| Publisher DOI: | 10.1016/j.physa.2021.126208 |
| Abstract: | In this paper, we explore the stability of the energy landscape of an Ising Hamiltonian when subjected to two kinds of perturbations: a perturbation on the coupling coe cients and external fields, and a perturbation on the underlying graph structure. We give su cient conditions so that the ground states of a given Hamiltonian are stable under perturbations of the first kind in terms of order preservation. Here by order preservation we mean that the ordering of energy corresponding to two spin configurations in a perturbed Hamiltonian will be preserved in the original Hamiltonian up to a given error margin. We also estimate the probability that the energy gap between ground states for the original Hamiltonian and the perturbed Hamiltonian is bounded by a given error margin when the coupling coe cients and local external magnetic fields of the original Hamiltonian are i.i.d. Gaussian random variables. In the end we show a concrete example of a system which is stable under perturbations of the second kind. |
| Rights: | ©2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | | http://creativecommons.org/licenses/by-nc-nd/4.0 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/90770 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 坂井 哲
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