6533b86ffe1ef96bd12cd0aa
RESEARCH PRODUCT
High-precision studies of domain-wall properties in the 2D Gaussian Ising spin glass
Hamid KhoshbakhtHamid KhoshbakhtMartin Weigelsubject
PhysicsHistorySpin glassSchramm–Loewner evolutionGaussianComputer Science ApplicationsEducationPlanar graphsymbols.namesakeThermodynamic limitsymbolsPeriodic boundary conditionsIsing modelBoundary value problemStatistical physicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-02-01 | Journal of Physics: Conference Series |