Non trivial overlap distributions at zero temperature
Abstract
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.
Cite
@article{arxiv.cond-mat/0006188,
title = {Non trivial overlap distributions at zero temperature},
author = {Silvio Franz and Giorgio Parisi},
journal= {arXiv preprint arXiv:cond-mat/0006188},
year = {2013}
}
Comments
9 pages, 8 figures; 3 references added, address corrected