Regensburg 2013 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 25: Critical Phenomena and Phase Transitions

DY 25.8: Talk

Thursday, March 14, 2013, 11:30–11:45, H46

Searching for spin-glass ground states in a transformed energy landscape — •Markus Manssen and Alexander K. Hartmann — Institut für Physik, Carl von Ossietzky Universität Oldenburg

Spin glasses and related models have been of interest to the scientific community for decades due to their inherent disorder and frustration and the resulting complex energy landscape. But this at the same time makes time evolution of these systems particularly slow and finding the ground states very hard (for 3D systems NP-hard in fact [1]). Consequently many elaborate algorithms have been developed to tackle these problems. Karandashev et al. [2] have proposed an inverse approach in which one takes a power of a system’s bond matrix, transforming its energy landscape to make finding the new ground state easier for any algorithm of choice. From there the original ground state should be easily reachable using the normal Hamiltonian. We test this method for the 3D binary Edwards-Anderson model with both the original authors preferred search algorithms and also Monte Carlo and parallel tempering simulations. We compare the results to the exact ground states. To evaluate the performance we have to also take the slow down caused by the transformed matrices into account.

[1] F. Barahona, On the computational complexity of Ising spin glass models, (J. Phys. A: Math. Gen. 15 3241, 1982)

[2] Ya.M. Karandashev and B.V. Kryzhanovsky, Transformation of energy landscape in the problem of binary minimization, (Doklady Mathematics, Vol. 80, No. 3, p. 927–931, 2009)