Stability of energy landscape for Ising models

Bruno Hideki Fukushima-Kimura, Akira Sakai, Hisayoshi Toyokawa and Yuki Ueda

Physica A: Statistical Mechanics and its Applications, 2021, vol. 583, issue C

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 coefficients and external fields, and a perturbation on the underlying graph structure. We give sufficient 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 coefficients 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.

Keywords: Stability; Spin glass; Ising model; Ground states (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:583:y:2021:i:c:s0378437121004817

DOI: 10.1016/j.physa.2021.126208

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