A new approach for the approximation of spin glass groundstates
We developed an algorithm called Cluster-Exact Approximation which calculates groundstates of 3d spinglasses with arbitrary nearest neighbour interactions up to sizes of . Its main idea is to construct unfrustrated clusters of spins, calculating their groundstate exactly using graphtheoretical methodes and iterating the scheme many times. In combination with genetic algorithms its possible to get to energetically very low lying states.
For three-dimensional realistic spin glasses (+/-J interaction) we found a complex ground-state landscape and evidence for an ultrametric organisatation of these states. Furthermore we were able to show that this kind of model has a stable spin glass phase for nonzero temperature by calculating the stiffness energy as function of the system size. For the two-dimensional model we found a complex ground-state landscape as well, but no ultrametric organisation.
Links to Spin Glass Servers
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