FisMat2017 - Submission - View

Abstract's title: Continuous variables on sparse graphs: a boost toward replica symmetry breaking
Submitting author: Cosimo Lupo
Affiliation: Dipartimento di Fisica, Sapienza Universita' di Roma
Affiliation Address: Piazzale Aldo Moro 5, 00185 Roma (RM)
Country: Italy
Oral presentation/Poster (Author's request): Oral presentation
Other authors and affiliations: Giorgio Parisi (Dipartimento di Fisica, INFN-Sezione di Roma1, CNR-Nanotec, Sapienza Universita' di Roma, Piazzale Aldo Moro 5, 00185 Roma (RM), Italia), Federico Ricci-Tersenghi (Dipartimento di Fisica, INFN-Sezione di Roma1, CNR-Nanotec, Sapienza Universita' di Roma, Piazzale Aldo Moro 5, 00185 Roma (RM), Italia)
Abstract

Vector spin glass models have been scarcely studied, mostly on fully connected topologies, which provide some unphysical predictions. We focus instead on diluted topologies, which yield more reliable results. By exploiting belief-propagation, we find that the XY model (the simplest vector model) is by far more unstable toward replica symmetry breaking (RSB), due to the combined effect of the graph sparsity and the spin continuous nature. Several interesting consequences arise, among which the appearance of RSB in the random field XY model and the recovering of the frequency density of vibrations in glasses in the zero–temperature limit.