Spin glasses with continuous variables on diluted graphs: A boost toward replica symmetry breaking.
Lupo C., Parisi G., Ricci-Tersenghi F.
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.