# Berlin 2012 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 22: Posters I

### DY 22.2: Poster

### Mittwoch, 28. März 2012, 17:00–19:00, Poster A

**Free-Energy Fluctuations and Chaos in the Sherrington-Kirkpatrick Model** — •Christoph Norrenbrock^{1}, Timo Aspelmeier^{1}, and Alexander K. Hartmann^{2} — ^{1}Georg-August-Universität Göttingen, Göttingen (Germany) — ^{2}Carl-von-Ossietzky Universität Oldenburg, Oldenburg (Germany)

We consider the mean-field Ising spin glass (Sherrington-Kirkpatrick model [1]) regarding its sample-to-sample fluctuations of the free-energy. It has been shown [2] that these fluctuations are related to bond chaos, which refers to the property that the equilibrium state changes completely by an infinitesimal change of the bond strength. Taking this connection into account, it has been shown analytically using replica methods [2] that the exponent µ, governing the growth of the fluctuations with the system size *N*, is bounded by µ≤1/4.

In contrast to previous studies (e.g. [3]), where the fluctuations in the mean-field model were investigated numerically at zero temperature only, we calculate µ at finite temperature by simulating chaos. For this purpose, we compute spin-overlaps between systems with slightly different bond-assignments. These systems (*N*=16 up to *N*=512) were simulated by Monte-Carlo simulations using the parallel tempering method.

Sherrington, D., Kirkpatrick, S., Phys. Rev. Lett. 35, 1792 (1975)

Aspelmeier, T., Phys. Rev. Lett. 100, 117205 (2008)

Boettcher, S., Eur. Phys. J. B 46, 501 (2005)