Phd in PHYSICS

Thesis title: Low energy excitations in Mean Field models of Vector Spin Glasses

The work of this thesis concerns the problem of linear low energy excitations of vector spin glass models. An analytical and numerical study is carried out, considering a fully connected random field Heisenberg model at zero temperature, a fully-connected vector p-spin glass model and a sparse random field Heisenberg model. We test these models against the low temperature behavior of finite dimensional glassy systems, in particular we show that these models posses phases where excitation spectra are gapped and the related eigenvectors are localised. In the case of the sparse model, we show that the density of states follow a quartic law at low frequency. In all models, the spin glass transition is characterised in terms of the behavior of the softest excitations. In the fully connected model the zero temperature spin glass transition in a field is a delocalisation transition of the softest modes. In the sparse case, a weak form of delocalisation appears.