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. Hartmann1 and A. Peter Young21University of Oldenburg, Germany — 2University 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).

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