Deformation of glassy states in p-spin models

In this master’s thesis we consider the p-spin spin glass model, in both its spherical and Ising versions, as a schematic model for amorphous solids. In the first part of the thesis, we briefly review the main properties of the spherical p-spin model, focusing in particular on the free energy landscape and the metastable/glassy states. We then introduce a model for studying the deformation of these glassy states, consisting in the addition of an s-spin term to the original p-spin Hamiltonian. This p + &#949;s deformation is then studied by considering the Franz-Parisi potential, which allows us to follow the glassy states and study their stability under the external perturbation.Considering first the spherical p-spin, a rich phase diagram is found by varying the degree of annealing (Tg) and the value of s. Fixing p =3, we find that for small s (s < 3) the glass yields in a replica-symmetric, elastic regime. However when s is increased to higher values, the glass may undergo a Gardner transition to marginal stability before yielding. The same analysis is carried out in the Ising p-spin, where we also find RS-stable yielding for s = 2, and a Gardner transition for higher values of s (s &#8805; 3). Monte carlo simulations, employing the planting technique, are performed to test some of the predictions in the elastic case.Finally, we consider how the formalism may be extended in order to characterise the fluctuations at the yielding point; this may be approached analytically in the spherical p-spin, while improved simulation techniques may be employed in the Ising p-spin in order to study the statistics of avalanches.