Non trivial overlap distributions at zero temperature

Details Non trivial overlap distributions at zero temperature Non trivial overlap distributions at zero temperature

2000-06-12

arxiv.org/abs/cond-mat/0006188v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 8 figures; 3 references added, address corrected

Scientific paper

10.1007/s100510070037

We explore the consequences of Replica Symmetry Breaking at zero temperature. We introduce a repulsive coupling between a system and its unperturbed ground state. In the Replica Symmetry Breaking scenario a finite coupling induces a non trivial overlap probability distribution among the unperturbed ground state and the one in presence of the coupling. We find a closed formula for this probability for arbitrary ultrametric trees, in terms of the parameters defining the tree. The same probability is computed in numerical simulations of a simple model with many ground states, but no ultrametricity: polymers in random media in 1+1 dimension. This gives us an idea of what violation of our formula can be expected in cases when ultrametricity does not hold.

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