# SKM 2023 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 49: Critical Phenomena and Phase Transitions

### DY 49.1: Vortrag

### Donnerstag, 30. März 2023, 15:00–15:15, ZEU 160

Metastate analysis for two-dimensional Ising spin glasses — •Alexander K. Hartmann^{1} and A. Peter Young^{2} — ^{1}University of Oldenburg, Germany — ^{2}University of California, Santa Cruz, USA

Spin glasses (SGs) are disordered magnetic systems which provide prototypical
models for complex systems, including systems outside physics such as neural networks
and machine-learning problems.
For the two-dimensional (2d) case, exact numerical ground states (GSs) of
large sizes
can be obtained by polynomial-time graph-matching algorithms.
Using these methods it was shown
that 2d SGs exhibit a spin-glass ordered phase only at zero temperature, see e.g. [1].
Results from applying a modified version of the GS algorithm
indicate that this phase is well described [2] by the so-called
“droplet” theory, i.e., it has a simple structure. Here, we consider
the *metastate* approach, which was introduced [3] to deal with the
chaotic size-dependence of the spin-glass state. By studying a large range of
sizes, we show convincingly that, in the thermodynamic limit,
spin correlations in a local region are
unaffected by the bonds far away, which is one of the main assumptions of the
droplet picture.

[1] A.K. Hartmann and A.P. Young, Phys. Rev. B 64, 180404 (2001).

[2] A.K. Hartmann and M.A. Moore, Phys. Rev. Lett. 90, 127201 (2003).

[3] C.M. Newman and D.L. Stein, J. Phys.: Condens. Matter 15, R1319 (2003).