Domain-wall excitations in the two-dimensional Ising spin glass

Hamid Khoshbakht, Martin Weigel

Research output: Contribution to journalArticle

11 Citations (Scopus)
15 Downloads (Pure)

Abstract

The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient implementations of combinatorial optimization algorithms to determine exact ground states for systems on square lattices with up to $10\,000\times 10\,000$ spins. While these mappings only work for planar graphs, for example for systems with periodic boundary conditions in at most one direction, we suggest here an iterative windowing technique that allows one to determine ground states for fully periodic samples up to sizes similar to those for the open-periodic case. Based on these techniques, a large number of disorder samples are used together with a careful finite-size scaling analysis to determine the stiffness exponents and domain-wall fractal dimensions with unprecedented accuracy, our best estimates being $\theta = -0.2793(3)$ and $d_\mathrm{f} = 1.273\,19(9)$ for Gaussian couplings. For bimodal disorder, a new uniform sampling algorithm allows us to study the domain-wall fractal dimension, finding $d_\mathrm{f} = 1.279(2)$. Additionally, we also investigate the distributions of ground-state energies, of domain-wall energies, and domain-wall lengths.
Original languageEnglish
Article number064410
JournalPhysical Review B
Volume97
DOIs
Publication statusPublished - 16 Feb 2018

Bibliographical note

Copyright © 2018 by American Physical Society. All rights reserved.
Individual articles may be downloaded for personal use; users are forbidden to reproduce, republish, redistribute, or resell any materials from this journal in either machine-readable form or any other form without permission of the APS or payment of the appropriate royalty for reuse. DOI: https://doi.org/10.1103/PhysRevB.97.064410

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

Keywords

  • cond-mat.dis-nn
  • cond-mat.stat-mech
  • physics.comp-ph
  • quant-ph

Fingerprint Dive into the research topics of 'Domain-wall excitations in the two-dimensional Ising spin glass'. Together they form a unique fingerprint.

  • Cite this