High-precision studies of domain-wall properties in the 2D Gaussian Ising spin glass

Hamid Khoshbakht, Martin Weigel

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Abstract

In two dimensions, short-range spin glasses order only at zero temperature, where efficient combinatorial optimization techniques can be used to study these systems with high precision. The use of large system sizes and high statistics in disorder averages allows for reliable finite-size extrapolations to the thermodynamic limit. Here, we use a recently introduced mapping of the Ising spin-glass ground-state problem to a minimum-weight perfect matching problem on a sparse auxiliary graph to study square-lattice samples of up to 10 000 × 10 000 spins. We propose a windowing technique that allows to extend this method, that is formally restricted to planar graphs, to the case of systems with fully periodic boundary conditions. These methods enable highly accurate estimates of the spin-stiffness exponent and domain-wall fractal dimension of the 2D Edwards-Anderson spin-glass with Gaussian couplings. Studying the compatibility of domain walls in this system with traces of stochastic Loewner evolution (SLE), we find a strong dependence on boundary conditions and compatibility with SLE only for one out of several setups.
Original languageEnglish
Article number012004
Number of pages11
JournalJournal of Physics: Conference Series
Volume1163
Issue number1
DOIs
Publication statusPublished - 26 Mar 2019
EventThird International Conference on Computer Simulations in Physics and beyond: CSP2018 - Moscow, Russian Federation
Duration: 24 Sep 201827 Sep 2018

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spin glass
domain wall
compatibility
boundary conditions
extrapolation
fractals
stiffness
statistics
exponents
disorders
thermodynamics
optimization
ground state
estimates
temperature

Bibliographical note

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd.

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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High-precision studies of domain-wall properties in the 2D Gaussian Ising spin glass. / Khoshbakht, Hamid; Weigel, Martin.

In: Journal of Physics: Conference Series, Vol. 1163, No. 1, 012004, 26.03.2019.

Research output: Contribution to journalArticle

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