Non trivial overlap distributions at zero temperature
The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, PO Box 563, 34100
2 Università di Roma "La Sapienza", Piazzale A. Moro 2, 00185 Rome, Italy
Corresponding author: a email@example.com
Published online: 15 December 2000
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.
PACS: 05.20.-y – Classical statistical mechanics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 75.10.Nr – Spin-glass and other random models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000