Probing ultrametricity in the low-temperature phase of finite-dimensional spin-glasses

by Andrea Maiorano (Dipartimento di Fisica, Università di Roma 'La Sapienza')

Thursday 27 Jun 2013, 10:30 → 11:30 Europe/Rome

Aula Rasetti (Dip. di Fisica)

Using results from very large scale numerical simulations of the three-dimensional Edwards-Anderson model performed on the Janus supercomputer, many predictions of the mean-field theory of spin glasses can be stringently tested. The numerical simulations produced a very large database of thermalized configuration for systems of unprecedented lattice sizes at temperatures down to 0.64T_c. Focusing on sample-to-sample fluctuations of the overlap probability distribution it is possible to measure any violation of constraints imposed by Stochastic Stability, Ultrametricity and Overlap Equivalence. Small deviations from predictions get actually smaller as system size increases. Ultrametricity can be also probed by introducing and accurately measuring three-replicas space correlation functions and studying the large-distance behavior. It has been also possible to study spin-spin correlation functions and measure the properties of connected clusters of very correlated sites, and to analyze the dependence on system size of the volume and surface of typical correlated clusters. Such clusters turn out to have very dense surfaces, compatible with being space filling in the thermodynamic limit.